LIBRARY 

OF    THE 

UNIVERSITY  OF  CALIFORNIA. 
Clcus 


. 


RAILWAY    RIGHT-OF-WAY 
SURVEYING 


BY 

ALBERT  I.  FRYE,  S.B.,  M.  AM.  Soc.  C.  E. 


NEW  YORK 

THE  ENGINEERING  NEWS  PUBLISHING  COMPANY 

1904 


Copyright,  1904, 

BY 
THE   ENGINEERING   NEWS   PUBLISHING   COMPANY 


PREFACE. 


THIS  little  book  outlines  a  modern  system  of  right-of-way  survey- 
ing, leveling,  and  mapping.  Though  the  system  as  a  whole  applies 
particularly  to  railroads,  the  ' '  adjustment  diagram ' '  feature  will  be 
found  useful  in  the  special  adjustment  of  streets,  canals,  highways, 
and  old  boundary  lines.  It  is  hoped  the  suggestions  here  given  will 
save  time  in  the  organization  and  prosecution  of  the  work  and  above 
all  will  lead  to  accurate  and  permanent  results. 

The  method  of  survey  herein  described  must  not  be  confused  with 
the  common  one  of  using  the  outside  head  of  rail  as  a  base  line  for 
locating  the  various  structural  features.  Vast  sums  of  money  have  been 
spent  for  such  surveys,  leaving  no  permanent  field  reference  to  lines 
run  and  recording  sets  of  maps  without  any  measurements  whatever. 
Many  of  them  have  been  ordered  under  the  directing  influence  of 
rushing  some  kind  of  survey  through  as  quickly  as  possible  for  pur- 
poses of  reconstruction,  hence  no  criticism  is  here  offered. 

But  there  is  no  excuse  whatever  for  property  surveys  not  referable 
to  fixed  base  lines,  whether  they  result  in  the  "scale  maps"  above 
referred  to  or  in  the  so-called  "very  complete  (?)  maps,"  showing 
instrument  lines  run,  angles  and  measurements,  "direct  from  the 
field  book."  The  former  class  of  maps  is  of  little  practical  value, 
while  the  latter  contains  a  mass  of  data  not  directly  available. 

The  simplest  system,  and  that  giving  the  most  accurate,  available, 
and  permanent  records,  is  one  that  reduces  the  important  field  meas- 
urements and  office  data  Jo  rectangular  coordinates  referred  to  an 
established  center  line.  This  is  the  system  here  presented. 

Without  some  definite  plan  of  rearranging  and  tabulating  data  as 
obtained,  much  time  will  be  lost  and  the  progress  of  the  work  greatly 


140390 


«v  PREFACE. 

•delayed.     For   this  purpose  the  Journal  and  Ledger  system  herein 
•described  is  invaluable  and  should  be  started  as  soon  as  possible. 

It  goes  without  saying  that  in  this  as  in  all  work  where  great 
accuracy  and  permanent  records  are  required,  progress  is  slow.  But 
.the  .results  as  they  appear  will  be  lasting. 

THE  AUTHOR. 

NEW  YORK,  September,  1904. 


CONTENTS. 


PACK 

INTRODUCTION vir 

Engineering  News  Article viii< 

Adjustment  Diagram viiii 

COLLECTING  THE  DATA i 

TENTATIVE  ALINEMENT  SHEET 2 

INDEXING  THE  DATA 4 

Note-books 4- 

Maps 5, 

Old  Papers 5. 

SEARCHING  DEEDS  AND  OTHER  RECORDS 6» 

Sample  Abstract  Sheet 6 

Field  Maps ; 6 

STANDARD  TAPE ". 7 

FIELD  INSTRUMENTS 8 

FIELD  WORK 9 

The  Practical  Center  Line 9 

Field  Adjustment  of  Center  Line 9 

Field  Work  for  Office  Adjustment 10 

Running  the  Base  Line 10 

Referencing  Instrument  Points 10 

Measuring  the  Base  Line 1 1 

Lateral  Field  Work u 

Base-line  Angles 12- 

Checking  the  Field  Notes 12- 

BOOKKEEPING  OF  THE  SURVEY 13: 

The  Journal 13: 

Description 13 

Calculations 14 

The  Adjusted  Stationing 15 

Monumenting  the  Adjusted  Center  Line i6> 

Setting  the  Monuments 16- 

The  Monument  Book 17^ 

The  Ledger 17 

Alinement  Sheet  (A) 17 

"  Old  Monument"  Sheet  (B) 18 

Structural  Sheet  (C) 20 


vi  CONTENTS. 

PAGE 

SlDE-MONUMENTING 21 

General  Discussion 21 

.     Where  to  Side -monument 21 

Side-monument  Sheet  (D) 22 

'CiTY  AND  TOWN  SURVEYS 23 

CONNECTING  WITH  GOVERNMENT  STATIONS 24 

LEVELING 25 

Establishing  Bench-marks 25 

Bench-mark  Sheet  (E) 25 

Elevations  of  Monuments 26 

Elevations  of  Track  and  Bridges - 26 

Physical  Features 26 

Side  Slopes 26 

Retaining  Walls 26 

Side  Levels 27 

THE  MAPPING 28 

The  Scale 28 

Land  and  Structural  Maps  Compared 28 

The  Land  Maps 29 

The  Paper 29 

Laying  out  the  Map 29 

Platting 29 

Old  and  New  Center  Lines 30 

Symbols 31 

Index  to  Transfers 31 

Property  Lines 32 

North  Point 32 

Explanatory  Notes 32 

Title .' 32 

A  Base  for  the  Structural  Maps 32 

The  Structural  Maps 32 

From  the  Land  Maps 33 

Structural  Features 33 

Economic  Method 33 

Physical  Features 34 

The  Index  Maps 34 

The  Alinement 34 

True  Bearings 34 

APPENDIX 37 

Hints  for  Field  Work 39 

Table  of  Temperature  Corrections 39 

Table  of  Allowable  Errors  in  Leveling 41 

Table  of  Natural  Tangents  and  Cotangents 42 

Table  of  Feet  and  Chains 44 

Trigonometric  Formulas 45 


OF  TNI 

INTRODUCTION.  (  WNiVERtlTY 

OF 


WHEN  a  railroad  line  is  located  the  real-estate  agent  is  furnished 
with  maps  more  or  less  complete  but  deemed  sufficient  for  his  imme- 
diate needs  in  purchasing  right  of  way.  Many  if  not  all  of  those  old 
maps  have  been  lost. 

Track  is  laid,  narrow,  broad,  or  standard  gage,  or  changed  from 
one  to  the  other  by  changing  one  rail  without  shifting  track  to  center. 
Perhaps  the  original  single  track  was  laid  on  the  old  center  line,  or 
perhaps  on  one  side  with  a  view  to  double-tracking  later.  The  original 
line  may  have  been  run  by  "the  needle"  in  a  serpentine  manner 
with  spasmodic  attempts  later  on  to  straighten  it  in  places,  leaving 
the  right-of-way  lines  anything  but  certain,  or  the  line  changed  alto- 
gether without  any  record  of  same. 

The  original  stationing,  in  any  case,  becomes  problematical,  the 
original  points  having  long  since  disappeared,  and,  further  to  com- 
plicate matters,  the  old  chain  was  too  long  or  too  short  by  several 
inches. 

Right-of-way  fences  have  been  built,  at  times,  inconsistent  with 
the  true  center  line,  producing  jogs  and  bends  here  and  there  in  the 
side  lines  intended  to  be  continuous  and  regular. 

The  Real-estate  Department  wrestles  with  these  problems,  falls 
back  upon  the  Law  Department  to  interpret  the  various  inconsistencies, 
and  the  latter  finally  concludes  that  too  much  time  is  being  wasted 
for  want  of  sufficient  accurate  data.  It  is  decided  that  the  cheapest 
and  best  way  is  to  have  a  survey  made,  comprehensive  in  character, 
in  order  to  straighten  out  the  numerous  land  complications. 

This  is  a  wise  decision.  The  general  manager  is  informed  that  in 
a  short  time  the  survey  will  be  found  to  produce  economic  results; 
that  is,  any  cost  of  such  work  is  economy  over  existing  methods. 

The  following  article  appeared  in  Engineering  News  of  April  14, 
1904,  and  is  inserted  here  as  introductory  to  the  general  discussion: 


Vlll 


INTRODUCTION. 


PRACTICE   IN   RE-ESTABLISHING   AND    MONUMENTING   A    RAIL- 
WAY CENTER  LINE. 

By  Albert  I.  Frye,  M.Am.Soc.C.E. 

The  value  of  re-establishing  and  monumenting  railroad  center  lines  is  recog- 
nized by  the  legal,  real-estate,  and  engineering  departments  of  Eastern  railroads 
as  an  economic  necessity.  It  crystallizes  and  harmonizes  the  actions  of  local  sur- 
veyors in  their  property  surveys  adjacent  thereto,  and  is  a  fitting  preliminary  to 
side-monumenting,  adjustment  of  track,  and  various  operations  incident  to  new 
work. 

The  writer  does  not  wish  to  enter  into  a  general  dissertation  upon  this  sub- 
ject, but  merely  to  bring  out  one  salient  feature  which  has  proved  convenient 
and  effective  in  adjusting  the  center  lines  of  tangents. 


ADJUSTMENT  DIAGRAM. 

An  "  instrument  line"  is  run,  say,  7  feet  north  of  and  parallel  with  an  "assumed 
center  line"  of  right  of  way,  and  all  monumental  landmarks,  such  as  old  monu- 
ments, fences,  track  centers,  centers  of  structures,  buildings,  etc.,  which  may 
be  reasonably  supposed,  to  have  been  placed  at  certain  distances  from  the  old  center 
line,  are  located.  The  ranges  and  stations  (rectangular  coordinates)  of  these 
points  are  calculated  with  reference  to  the  "assumed  center  line."1 

On  a  longitudinal  scale  of,  say,  800  feet  to  an  inch  the  "assumed  center  line" 
is  laid  off,  the  lateral  scale  being  i  foot  to  i  inch.  The  various  points  which  have 
been  located  and  calculated  are  then  platted  from  the  "assumed  center  line," 
the  lateral  distance  being  the  difference  between  the  range  as  calculated  and  its 
supposed  original  distance  from  the  old  center  line.  For  instance,  if  the  range 
of  an  old  fence  were  found  to  be  49.75  feet  north  of  assumed  center  line,  whereas 
it  was  supposed  to  have  been  placed  50  feet  distant,  then  the  fence  at  that  point 
would  tend  to  establish  the  center  line  0.25  foot  south  of  the  "assumed"  and  the 
point  would  be  platted  "range  0.25  south." 

It  is  essential  to  classify  the  various  landmarks  used  and  further  to  distinguish 
those  found  on  the  north  side  of  right  of  way  from  those  on  the  south,  connecting 
each  class  on  either  side  of  right  of  way  by  its  characteristic  (colored)  line. 


See  page   14. 


INTRODUCTION. 


IX 


The  following  notation  has  been  used  with  success: 


A.   (black  line) 


=-  Assumed  center  line. 


R.  (full  brown  line)  = 
r.  (dotted  brown  line)  = 
P.  (full  yellow  line)  = 
p.  (dotted  yellow  line )  =- 
M.  (full  blue  line) 
m.  (dotted  blue  line)  «= 
S.  (full  green  line)  - 
T.  (full  pencil  line)  - 
C.  (full  red  line) 


Railroad  fences  on  north  side  of  right  of  way. 
Railroad  fences  on  south  side  of  right  of  way. 
Private  fences  on  north  side  of  right  of  way. 
Private  fences  on  south  side  of  right  of  way. 
Monuments  on  north  side  of  right  of   way. 
Monuments  on  south  side  of  right  of  way. 
Existing  structures. 
Existing  tracks. 
Adjusted  center  line. 


Center  line  as 
would  be  es- 
tablished by 


The  accompanying  simple  sketch  will  serve  to  illustrate. 

The  adjusted  center  line  is  best  perfected  (after  all  the  others  are  platted)  by 
the  use  of  a  fine  thread,  and  in  a  manner  similar  to  establishing  grades  on  pro- 
files. The  lateral  scale  adopted — i  inch=i  foot — insures  great  accuracy.  It 
must  be  remembered  that  all  the  lines  shown  are  actual  possible  center  lines  cross- 
ing and  recrossing  each  other  in  a  maze  of  network  and  are  in  no  sense  offset 
lines,  hence  the  final  adjustment  is  a  direct  one. 

The  object  in  distinguishing  the  north  monumental  points  from  those  on  the 
opposite  side  of  right  of  way  is  to  avoid  encroachment. 

As  frequently  happens  with  long  "tangents"  run  in  the  early  days,  the  re- 
adjustment necessitates  a  slight  "bend"  the  position  of  which  should  be  fixed 
at  some  "round"  station  by  a 'stone  monument.  The  semi-graphical  method 
above  described  readily  points  to  the  position  of  such  a  bend,  and  leaves  a  perma- 
nent record  of  existing  facts  and  conclusions  drawn.  The  center  line  being  thus 
fixed  is  permanently  monumented  on  the  ground. 


RAILWAY   RIGHT-OF-WAY  SURVEYING. 


COLLECTING  THE  DATA. 

BEFORE  starting  in  the  field  it  will  be  well  to  become  familiar  in  a 
general  way  with  the  nature  and  amount  of  work  to  be  accomplished, 
as  well  as  the  data  at  hand  and  necessary  to  be  obtained  in  order  to 
accomplish  it.  These  data  should  be  classified  and  indexed  system- 
atically, care  being  taken  to  record  the  date  of  each  document  or 
item,  as  much  of  its  value  may  depend  upon  the  year  or  even  the  month 
of  its  origin. 

A  careful,  systematic  search  should  be  made  in  the  several  offices 
of  the  company  for  note- books,  plans,  letters,  papers,  or  documents 
of  any  kind  which  supposedly  bear  upon  the  problem  of  fixing  the 
center  line  or  adjusting  the  various  land  lines.  Sometimes  a  paper 
or  letter  relating  almost  wholly  to  construction  matters  will  aid  mate- 
rially in  clearing  up  the  adjustment  of  a  tangent. 

City  and  county  records  must  be  examined  for  deeds  and  maps. 
If  a  former  county  has  been  divided,  this  fact  must  be  noted  in  the 
searching.  Copies  of  all  city  and  tax  maps  should  be  had. 

Much  valuable  information  will  be  gathered  along  the  line  from 
surveyors  and  others  incidentally  as  the  work  proceeds,  and  a  diary 
or  note-book  should  be  kept  for  this  purpose. 

Prior  to  indexing,  a  tentative  alinement  sheet  should  be  made  up 
f ;  om  the  filed  location  of  the  line  or  from  any  authoritative  data,  num- 
bering the  tangents  consecutively  from  the  beginning  of  the  line  or 
station  zero  of  the  new  survey.  Of  course  this  will  be  superseded 
by  the  regular  "Alinement  Sheet  (A)"  of  the  ledger,  described  later. 


TENTATIVE  ALINEMENT  SHEET. 


The  tentative  alinement  sheet  will  be  compiled  from  existing  records 
and  will  represent,  merely,  the  old  and  new  theoretical  alinements, 
preliminary  in  character,  to  serve  as  an  aid  to  indexing  and  for  both 
field  and  office  reference.  Generally,  the  new  alinement  should  follow 
the  center  line  as  it  will  be  monumented  later,  while  the  old  will  usually 
be  the  line  as  filed.  Even  if  the  two  be  not  identical,  the  former  should, 
preferably,  be  the  center  of  the  present  100  feet  right  of  way.  There 
may  be  exceptions  to  this  rule,  however,  depending  somewhat  upon 
the  position  of  the  track. 

The  sheet  should  contain  information  as  per  following  headings  of 
columns: 

1.  Tangent  No. 

2.  Nearest  depot. 

3.  Approximate  location. 

4.  New  stationing. 

5.  Point,  P.C.  or  P.T. 

6.  Length  of  curve  in  feet. 

7.  Degree  of  curve. 

8.  Tangent  distance  (semi-tangent). 

9.  Intersection  angle  (/). 

10.  Length  of  tangent  in  feet. 

11.  Length  of  tangent  in  miles  and  tenths. 

12.  True  course  of  tangent. 

13.  Monument  to  be  set. 

14.  Distance  to  old  center  line  N.  or  S. 

15.  Old  stationing  of  new  monument  points. 

16.  Old  stationing  of  old  P.C.  or  P.T. 

17.  New  stationing  of  old  P.C.  or  P.T. 

1 8.  Length  of  old  curve  in  feet. 

19.  Old  intersection  angle  (7). 

20.  Tangent  distance  (semi-tangent). 

21.  Length  of  old  tangent  in  feet. 

22.  Reference  to  notes,  maps,  etc. 

23.  Remarks. 


New  alinement.  ^ 


Old  alinement. 


TENTATIVE   ALINEMENT   SHEET.  3 

Note.— The  line  items  will  be  for  new  P.C.'s,  P.T.'s,  and  monu- 
ments to  be  set  on  the  new  center  line.  Monuments  should  be  set  at 
"round  stations"  from  1000  to  2000  feet  apart  on  tangents  and  from 
500  to  800  feet  apart  on  curves,  also  at  beginning  and  end  of  curves 
or,  if  impracticable,  near  same  for  reference.  For  Column  No.  13 
the  kind  of  monument  will  be  noted  as  "Stone"  for  stone  monument, 
etc.  The  equation  between  the  old  and  new  stationing  at  these  points 
may  be  obtained  from  4  and  15. 


INDEXING  THE  DATA. 


FIELD  BOOKS,  especially  old  ones,  and  particularly  those  of  a  semi- 
private  character  if  any  exist,  should  be  carefully  examined  for  in- 
formation regarding  the  center  line,  any  monuments  which  may  have 
been  set  .or  located,  land  surveys,  etc. 

They  should  be  indexed  in  detail,  by  pages,  on  a  general  index 
sheet,  referring  to  the  numbered  tangents  as  per  the  tentative  aline- 
ment  sheet,  and  in  such  a  manner  that  they  may  readily  be  selected 
for  field  or  office  work. 

The  following  system  has  been  found  well  adapted  for  such  refer- 


ence : 


INDEX  TO  NOTE-BOOKS. 


Tang. 

Description. 

Date. 

Book. 

Pg. 

Specia 

1  Use. 

Remarks. 

No. 

Field. 

Office. 

6 

Correct  notes  of  Slater 
property  

4.—  24.—  71 

2<;K 

•27 

Maps 

«! 

47 

Monument  350  ft.  E.  I 
of  Ave.  G  I 
Land  lines,   B    &  S. 
crossing  

Aug.,  1877 

1-8-Q2 

32M 
4iP 

•I 

82 

Center 
line 

Maps 

Valuable 

Similarly,  the  old  maps  should  be  indexed  under  a  new  system  of 
numbers,  but  also  retaining  the  old  in  the  index  book.  The  number 
will  comprise  the  number  of  the  tangent  to  which  the  map  belongs 
by  location,  with  a  distinguishing  letter  suffixed. 

The  plans  are  classed  according  to  tangent  numbers  both  as  re- 
gards indexing  and  filing.  The  numbers  are  suspended  from  the  plans 
on  tags,  thus  allowing  the  direct  selection  of  plans  pertaining  to  any 
tangent  without  being  obliged,  necessarily,  to  resort  to  the  index. 

The  following  simple  system  will  illustrate: 

4 


INDEXING   THE   DATA. 
INDEX  TO  MAPS. 


Tang. 

No. 

Description. 

New 
No. 

Scale. 

Date. 

Plan- 
Kind. 

Old 

No. 

Remarks. 

4 

Old  line  of  R.R.  atD. 
Canal  crossing 

4.n 

IOO 

r_g_68 

Trac. 

C  16 

"1 

Burgess  property  at 
Clifton  

Ub 

80 

4-3-85 

j  Blue- 
\  print 

lE6 

j  Valuable 
1  for  field 

OLD  PAPERS. 

Papers  which  have  been  in  the  archives  of  the  company  for  years 
undisturbed  and  of  ancient  date,  also  loose  notes  of  positions  of  old 
monuments  and  corners,  or  any  information  relating  to  land  lines  or 
lines  in  general  which  may  appear  to  have  value,  may  be  placed  in 
envelopes  and  numbered  by  tangents  as  above. 

Sometimes  a  long  tangent  may  require  several  envelopes  and  it 
may  be  more  convenient  to  classify  or  even  index  the  papers  either 
as  regards  position  on  the  tangent  or  according  to  the  class  of  data 
which  the  paper  contains. 


SEARCHING  DEEDS  AND  OTHER  RECORDS. 

ONE  of  the  most  important  operations  is  that  of  searching.  Ab- 
stracts of  all  deeds  should  be  made  in  duplicate,  one  for  the  field  and 
one  for  the  drafting-room.  These  sheets  may  be  of  fairly  large  size, 
say  6"X8",  typewritten,  and  with  holes  at  the  top  for  filing. 

First  come  the  headings,  next  the  description,  and  lastly  the  special 
clauses,  thus: 

SAMPLE  ABSTRACT  SHEET. 

Tangent  No City  or  town County 

Date Map  No Record  Book,  pg 

Kind  of  Deed Office  Rec.  Bk.,  pg Office  No.  of  Deed .... 

Grantor \ Grantee 

Description 

Special  clauses 


FIELD  MAPS. 

In  connection  with  the  field  copies  of  abstracts  there  should  be 
accompanying  maps,  on  tracing-cloth,  of  each  tangent  with  included 
portions  of  adjacent  curves.  These  maps  may  be  drawn  to  a  small 
scale  for  convenience,  say  200  feet  to  an  inch,  showing  streets,  com- 
pany properties  with  the  map  number  of  each  lot  as  per  abstract,  all 
vital  measurements,  such  as  width  of  right  of  way,  change  in  center 
line,  positions  of  any  monuments  referred  to  in  deeds  or  other  records, 
and  in  fact  any  "map  information"  which  may  be  useful  in  the  field. 

Where  reference  is  made  to  monuments  they  should  be  hunted  up 
in  the  field  in  advance  of  the  regular  field  work. 

6 


STANDARD  TAPE. 

A  IOO-FOOT  steel  tape  graduated  to  hundredths  of  a  foot,  properly 
certified  to  as  correct  as  a  certain  temperature,  say  60°,  and  at  a; 
certain  tension,  say  10  pounds  when  entirely  supported,  should  be 
kept  in  the  safe  absolutely  free  from  field  work  and  used  as  a  test  tape 
only. 

It  is  far  preferable  to  a  standard  base  with  fixed  ends  in  that  no 
temperature  correction  is  necessary,  and  it  only  remains  to  give  both 
tapes,  the  standard  and  the  one  being  tested,  the  same  pull  in  order 
to  eliminate  tension  as  well  as  temperature  correction. 

Of  course  this  does  not  do  away  with  the  use  of  the  spring-balance 
or  thermometer  in  the  field  where  great  accuracy  is  required,  as,  for 
instance,  measuring  long  base  lines,  making  city  surveys  or  surveys 
for  legal  purposes. 

It  is  well  to  keep  in  mind  that  a  change  in  temperature  of  about 
15°,  or  tension  of  6  to  10  pounds  (depending  upon  the  area  of  cross- 
section  of  tape),  will  produce  a  change  in  length  of  yj^  of  a  foot  in  a 
loo-foot  steel  tape;  hence  for  long  measurements  a  considerable  error 
might  accumulate  if  left  uncorrected. 

7 


FIELD  INSTRUMENTS. 

ALL  field  instruments  should  be  first  class. 

The  steel  tapes  should  be  graduated  throughout  to  hundred ths. 
The  zoo-foot  tapes  should  be  detachable  from  the  box  and  be  pro- 
vided with  handles  for  both  ends.  As  they  will  be  used  considerably 
in  measuring  long  base  lines,  the  zero  mark  should  come  at  the  end 
of  the  steel  ribbon  itself  and  not  at  the  end  of  an  uncertain  brass  ring. 
The  5o-foot  tapes,  for  minor  measurements,  may  have  the  brass  ring 
if  preferred. 

The  transits  should  be  heavy  and  be  provided  with  powerful  tele- 
scopes if  long  tangents  are  to  be  run.  A  i2-ounce  plumb-bob  is  not 
too  heavy. 

Flag-poles  of  the  ordinary  kind,  both  wood  and  iron,  are  generally 
convenient,  but  for  running  long  tangents  flag-boards,  say  6  inches 
wide  and  provided  with  iron  shoes  properly  centered,  are  necessary, 
or  even  at  times  a  board  10  or  12  inches  wide  is  called  for.  The  latter 
need  not  be  shod,  however.  The  boards  should  be  checkered  red 
and  white  alternately,  with  well-defined  vertical  center  lines,  the  hori- 
zontal lines  dividing  the  colors  being  spaced  about  the  width  of  the 
board  apart.  Such  boards  can  be  plainly  sighted  on  clear  days  "  with 
the  sun"  about  i?  to  2j  miles. 

Standard  survey-tacks  with  a  depression  in  the  middle  are  far 
preferable  to  the  ordinary  and  should  be  used  for  instrument  or  flag- 
pole points. 

Yellow  crayon  is  the  best  for  marking. 

8 


FIELD  WORK. 

THE  PRACTICAL  CENTER  LINE. 

IN  re-establishing  a  railway  center  line  it  is  essential  to  preserve 
in  the  main  the  line  recognized  as  existing  on  the  ground,  evidenced 
by  monuments,  fences,  buildings,  bridges,  tracks,  stakes,  etc.  As  in 
every  problem  there  is  a  theoretical  and  a  practical  side,  so  in  this 
the  filed  location  is  the  theoretical,  while  the  existing  landmarks  may 
be  said  to  determine  the  practical  location.  The  practical  location 
governs. 

Generally  it  will  be  necessary  only  to  establish  the  center  lines  of 
two  adjacent  tangents,  connecting  them  with  the  theoretical  curve  of 
filed  location.  If  this  latter,  however,  does  not  reasonably  fit  the 
practical  curve  on  the  ground  as  evidenced  by  controlling  landmarks, 
then  it  may  be  necessary  to  alter  the  radius  or  degree  of  the  curve 
accordingly,  especially  if  it  is  a  very  long  one.  Inaccuracy  in  former 
field  work,  long  preserved  and  unconnected,  as  when  right-of-way 
fences  are  being  built,  would  allow  the  practical  to  take  precedence. 

Of  course  any  radical  departure  from  curve  of  filed  location  should 
be  avoided  if  possible,  and  this  may  best  be  effected  in  some  cases  by 
a  slight  alteration  of  one  or  both  of  the  adjacent  tangents. 

FIELD  ADJUSTMENT  OF  CENTER  LINE. 

In  many  cases  the  center  line  can  be  established  directly  in  the 
field,  and  this  should  be  done  where  practicable,  as  the  instrument  line 
will  then  be  a  parallel  offset  to  the  true  center  line,  thus  simplifying 
or  avoiding  many  office  calculations. 

A  short  tangent  with  few  controlling  landmarks,  but  definite  and 
consistent  in  themselves,  offers  a  favorable  illustration  for  field  adjust- 
ment. Points  on  the  true  center  line  or  on  an  offset  line  are  set  off 
from  the  landmarks  by  knowing  their  assumed  positions,  and  an  in- 
strument line  run  directly  in  the  field  along  "these  points,"  correcting 
any  inconsistencies  and  giving  due  weight  to  the  most  important. 

If  this  cannot  be  done,  then  a  center  line  may  be  assumed  as  nearly 
as  possible  and  an  instrument  line  run  parallel  with  it,  the  various 

9 


10  RAILWAY   RIGHT-OF-WAY   SURVEYING. 

landmarks  located  and  the  line  adjusted  in  the  office  as  explained  in 
the  Introduction. 

FIELD  WORK  FOR  OFFICE  ADJUSTMENT. 

The  instrument  line  may  be  run  in  the  middle  of  one  of  the  outside 
main  tracks  for  safety  and  so  that  the  various  points  on  the  line  may 
be  established  by  "tacks  in  ties"  instead  of  by  driving  stakes.  By 
experience  it  has  been  found  that  track  ties,  when  well  ballasted,  will 
hold  their  position  fairly  well  and  much  better  than  ordinary  stakes, 
especially  during  periods  of  frost,  with  the  added  advantage  of  rapid 
work  and  a  level  support  for  measuring  along  the  instrument  or  base 
line. 

Of  course  track  foremen  must  be  notified  not  to  tamp,  shift,  or  in 
any  manner  disturb  the  track  or  ties  during  the  operation. 

Running  the  Base  Line. — If  the  tangent  is  not  too  long  for  a  dis- 
tinct sight  from  one  end  to  the  other,  the  line  may  be  run  by  "  following 
up"  with  the  transit,  with  the  sun  on  the  foresight,  fixing  well-centered 
points  from  1000  to  2000  feet  apart.  Preferably  these  points  should 
be  opposite  or  near  points  to  be  monumented  on  the  center  line,  the 
monuments  for  which  have  previously  been  distributed  on  the  ground. 

For  long  tangents  it  is  well  to  begin  in  the  middle,  establishing 
two  points  as  far  apart  as  practicable,  and  work  in  either  direction 
toward  the  ends  by  reversing  the  instrument.  The  method  of  reversing 
may  be  "four  sights  to  right,"  then  turn  half-round  and  "four  sights 
to  left,"  preserving  the  order  of  reversing,  infallibly. 

The  engineer  in  charge  may  be  with  the  front  flag  and  be  provided 
with  a  field-glass  to  catch  signals  from  the  transit.  If  the  instrument 
be  out  of  adjustment,  the  true  point  will  be  midway  between  the  average 
of  each  set  of  points  provided  they  be  given  equal  weight. 

A  signal  for  repetition  of  right  or  left  sights  may  be  called  for  by 
the  front  flagman  by  dropping  his  handkerchief  intermittently  to  the 
right  or  left  side  the  required  number  of  times.  This  motioning  will 
not  be  confused  with  the  "general  wave  signal"  for  calling  up. 

An  extra  man  for  transmitting  signals  or  messages  is  sometimes 
desirable,  and  the  back  flagman  may  also  be  provided  with  a  field- 
glass  or  engineer's  level  to  watch  for  signals. 

Referencing  Instrument  Points. — Points  on  the  instrument  line 
near  center-line  stations  to  be  monumented  should  be  referenced  very 
substantially,  soon  after  the  line  is  run  and  prior  to  the  general  field 
work,  as  they  will  be  used  later  in  setting  the  monuments.  The  refer- 
ence should  be  by  at  least  two  lateral  measurements  to  preserve  the 


FIELD  WORK.  II 

line,  which  is  most  important,  and  by  two  or  more  diagonal  measure- 
ments. Good  sound  ties  should  be  selected  for  these  reference  points, 
well  marked  with  paint  or  crayon,  and  the  matter  explained  to  the  sec- 
tion foreman. 

Measuring  the  Base  Line. — Intermediate  points  will  be  set  on  the 
base  line  a  little  less  than  300  feet  apart,  so  three  measurements  of  the 
loo-foot  t ape  will  stretch  between.  They  should  be  marked  by  standard 
tacks  accurately  centered  for  line,  to  be  used  later  as  transit  points 
for  lateral  field  work.  These,  together  with  those  referenced  near 
monument  points,  should  be  lettered  consecutively,  A,  B, .  . .  Y,  Z;  AA, 
AB,  .  .  .  AY,  AZ\  BA,  BB,  .  .  .  etc.,  throughout  the  tangent,  on  the 
ties,  and  on  near-by  telegraph  poles,  buildings,  and  fences  along  the  right 
of  way.  The  same  lettering  is  of  course  recorded  in  Ihe  field  book. 
The  tacks  in  ties  should  also  be  plainly  marked  with  a  heavy  surround- 
ing triangh  o  yellow  crayon. 

The  method  of  measuring  the  base  line  and  keeping  the  notes  must 
be  systematic  and  very  exact.  A  very  simple  system  is  to  measure 
from  one  "3oo-foot"  point  to  the  next  and  then  back,  keeping  the 
measurements  in  two  columns,  taking  the  average  of  the  results,  making 
the  proper  temperature  correction,  and  putting  the  final  corrected  re- 
sult on  the  line  itself,  immediate  y,  thus: 


A  to  B. 
97-795          97-796 
99.632          99-631 
94.538          94.536 

B  to 
99.832 
99-524 
94.316 

C. 

99.836 
94.313 

Temp. 

291.965         291.963 
291.964 
corr.        .  024 

293.672 

293- 
Temp.  corr. 

293.674 

673 
025 

Center  Lint 

291.988 

P 

293- 

698 

| 

„         S9I.99 

InstUne 

\ 

^- 
* 

3- 
S 

1 

Lateral  Field  Work. — From  these  points  A,  B,  C,  etc.,  on  the  base 
line,  the  side  monumental  features  are  located.  As  with  the  base  line 
itself,  all  measurements  should  be  taken  and  recorded  in  the  same 
manner  and  the  corrected  measurements  set  down  immediately  on 


12 


RAILWAY    RIGHT-OF-WAY   SURVEYING. 


the  lines  measured.     Angles  should  be  at  least  doubled,  as  a  check, 
no  matter  how  close  the  object. 

A  good  system  is  to  set  down  the  angles  to  Ihe  object  above  the 
measurements  to  same,  and  the  corrected  measurements  on  the  sketch 
itself.  The  angles  to  objects  may  be  designated  by  the  letter  name 
of  the  instrument  point  on  the  base  line,  with  the  suffixes  "sub  i," 
"sub  2,"  etc.,  where  more  than  one  angle  is  turned  from  the  same 
point,  thus: 


Cen+er  Line 


Stone 
Mon. 

B, 

112-32-30 
225-05-00 


Call  112-32-30 

65-327  65.329  57. 

65.328 
Temp.  corr.     .005  Temp.  corr. 


52-16-00 
104-32-3° 

Call    52-16-15 
>6  57.423 

57-424 
.004 


65-323 


57-420 


Note.  —  The  length  of  tape  should  be  recorded  on  each  page,  as, 
for  instance,  "Tape  correct  at  63°  and  TO  Ibs."  l  As  tapes  are  often 
exchanged,  this  becomes  very  necessary.  Also  the  field  temperature 
of  the  ground  must  be  recorded  for  each  page,  and  often  for  each  line 
measured,  as  the  case  may  demand. 

Base-line  Angles.  —  Angles  in  the  instrument  or  base  lines,  as 
chords  connecting  tangents,  should  be  measured  by  ten  continuous 
readings,  and  these  must  be  examined,  by  subtraction,  for  "slip"  before 
dividing  the  final  reading  by  its  number. 

Checking  the  Field  Notes.  —  The  field-book  notes  should  be  checked 
as  soon  as  possible,  using  a  check-mark  with  the  initial  of  the  checker 

TT        , 

therein;  thus,  A/  means,  checked  by  "H,"  or  Harris. 

The  check  should  be  after  every  item  and  not  simply  once  at  the 
bottom  of  the  page. 

1  Tension. 


BOOKKEEPING  OF  THE  SURVEY. 

IN  a  survey  of  this  character  it  would  be  the  height  of  folly  to  plat 
the  field  notes  directly  on  the  maps  "just  as  they  are  taken  in  the  field." 
The  author  has  seen  such  work  and  heard  arguments  put  forth  in  its 
favor,  but  has  always  discouraged  it. 

The  field  notes  are  merely  a  means  to  an  end  and  not  the  end  itself. 
The  field  book  corresponds  to  the  day  book  of  a  business  firm  and 
should  have  an  accompanying  journal  and  a  ledger.  Imagine  an 
accountant,  at  the  end  of  the  year,  exhibiting  his  day  book  to  the 
manager  as  a  clear  and  concise  statement  of  the  firm's  business!  Yet 
this  is  a  fair  illustration  of  the  above. 

In  addition  to  the  journal  and  ledger,  a  monument  book  should 
be  kept,  as  will  be  explained  later. 

THE  JOURNAL. 

A  very  convenient  system  of  office  record  is  to  have  the  line,  as  it 
is  developed  by  the  survey,  platted  in  a  large  cross-section  book,  or 
journal,  the  pages  large  enough  to  embrace  (on  a  reduced  scale)  the 
outline  of  the  right-of-way  map. 

For  instance,  suppose  we  wish  to  adopt  a  5o-foot  scale  for  the  maps 
themselves,  making  them,  say,  28"X42"  inside  of  border  line  and  leav- 
ing a  £-inch  margin  all  round.  This  will  economically  use  58"  Paragon 
mounted  paper,  which  is  really  59"  wide. 

Description. — A  handy  journal  for  such  size  maps,Jand  one  which 
has  been  found  satisfactory,  is  as  follows:  Pages  io,f'X  16.4",  with 
cross-section  lines  spaced  5.8  to  the  inch.  Using  a  platting  scale  of 
one  space  to  25  feet,  four  spaces  per  100  feet,  the  full  area  of  the  map 
may  be  shown  in  size  9§"Xi4i",  thereby  leaving  plenty  of  margin. 
It  may  contain  about  200  pages,  covering  about  15  miles  of  line.  It 
should  have  durable  leather  binding. 

A  "map  sheet"  outline  may  be  shown  on  every  fourth  page  of  the 
journal  corresponding  in  area  (and  approximately  in  number)  with 
the  right-of-way  maps  to  be  platted,  using  the  reduced  scale  as  pre- 
13 


14  RAILWAY    RIGHT-OF-WAY   SURVEYING. 

viously  mentioned.  For  instance,  sheet  No.  i,  corresponding  to  right- 
of-way  map  No.  i,  may  be  platted  on  page  7,  sheet  2  on  page  n,  3 
-on  15,  etc.,  leaving  some  pages  in  the  front  of  the  book  for  indexing, 
and  the  intermediate  pages,  between  the  "map  sheets,"  for  calculations 
of  surveys  near  their  respective  localities,  also  for  calculations  of 
curves  connecting  tangents,  etc. 

Calculations. — On  the  page  directly  opposite  each  "map  sheet," 
as,  for  instance,  on  page  6  opposite  sheet  No.  i,  sketches  of  location 
of  all  important  landmarks,  taken  from  the  field  notes,  should  be 
shown,  preferably  opposite  their  true  positions  on  page  7.  Calculations 
of  rectangular  co-ordinates  of  these  landmarks,  referred  to  the  instru- 
ment line,  assumed  line,  and  adjusted  center  line,  should  accompany 
the  sketches  if  there  is  room  on  the  page;  if  not,  the  results,  simply, 
may  be  recorded.  The  former  method  is  far  preferable. 

Calculations  are  considered  checked  only  when  evidenced  by  the 
regular  check-mark  with  the  initial  of  the  checker. 

If  the  center  line  is  to  be  adjusted  in  the  office,  the  calculations 
should  be  made  in  some  neat  form  with  sketch  as  follows,  showing 
instrument  line,  assumed  center  line,  and  location  of  landmark: 


Fence  Corner} 

ff=     +44M  \Tcmg.#6 

5=777+20.701       * 


Assumed  CeriferLine 


Jnst  Line 


Range. 

Log       177.40=2.2489536 
Sin    23-13-20  =  9.5958250 


Station. 

=  2  .  2489536 
08  =  9.9633072 


69.948 


Assumed. 
69.948 
20. 

+  49 • 948 


1.8447786 

Adjusted. 
69  .  948 
20.087 


163 . 027 
Assumed. 

££=778+93. 76 
l      63.03 


2.2122608 

Adjusted. 
778+92.79 
i      63.03 


=  +  49.861 


777+3°-73        5=777+29.76 


The  above  shows  at  a  glance  the  range  and  station  of  the  fence 
corner  from  the  instrument  line,  from  the  assumed  line,  and  from  the 
adjusted  center  line,  referred  to  Tangent  No.  6.  "Assumed  line" 
ranges  and  stations  are  used  in  platting  the  "adjustment  diagram" 
before  the  adjusted  ranges  and  stations  can  be  obtained. 


BOOKKEEPING   OF   THE   SURVEY.  1$ 

Monuments  and  other  landmarks  are  likewise  treated  in  the  same 
manner. 

The  assumed  ranges  of  the  various  points  located  are  very  easily 
determined,  of  course,  by  taking  into  account  the  instrument-line 
offset  from  the  assumed.  The  assumed  stationing  is  obtained  by 
intersecting  the  assumed  center  line  (by  chord  connection)  with  the 
adjusted  center  line  of  the  previous  tangent,  calculating  the  connect- 
ing curve  and  the  positions  of  its  P.C.  and  P.T.  with  reference  to  ad- 
jacent instrument  points  of  the  survey,  and  carrying  the  stationing 
around  the  curve  from  the  previously  adjusted  tangent  to  the  imme- 
diate tangent  under  consideration. 

Of  course  this  is  all  tentative.  The  adjustment  diagram  may 
then  be  platted,  the  adjusted  center  line  determined,  and  from  a  new 
calculated  intersection  with  the  previous  tangent  the  corrected  or 
adjusted  stationing  may  be  projected. 

The  Adjusted  Stationing. — Having  determined  the  adjusted  station- 
ing of  the  first  instrument  point  on  the  base  line  (opposite  same  station 
on  the  adjusted  center  line),  as,  for  instance,  point  DA  (765+52.31), 
the  stationing  of  the  other  points  can  generally  be  determined  by 
adding  the  base-line  distances  between  the  points,  as  follows: 

Adjusted  Stationing.         Inst.  Points.  Check. 

765+52.31  DA 

2       90.91 


768+43.22  DB  290.91 

2     96.43  296.43 

291.32 

771+39.65  DC  298.79 

2     91.32  294.13 

295.14 
774+30.97  DD  299.56 

2     98.79 
2066.28 


777+29.76  DE 

2       94.13 


780+23.89  DF  765+52.31 

2       95.14  20       66.28 


783+19.03  DG  786+18.59 

2       99.56 

786+18.59  DH 

A  table  similar  to  the  above  should  be  made  on  every  map  sheet 
of  the  journal  and  thoroughly  checked,  using  the  characteristic  check- 
mark and  initial  of  the  checker. 


1 6  RAILWAY   RIGHT-OF-WAY   SURVEYING. 

From  these  tables  the  adjusted  stations  of  the  several  landmarks 
are  determined  in  connection  with  the  previously  explained  calcu- 
lations, and  the  results  set  down  adjacent  to  the  monumental  points 
on  the  calculation  sketches  and  on  the  map  sheets. 

It  is  very  desirable  to  transfer  these  stations  in  red  ink  to  the  in- 
strument-line points  in  the  field  books  for  ready  reference.  Of  course 
they  are  not  strictly  the  stations  of  these  points,  but  of  points  opposite 
on  the  center  line.  The  angle  between  the  instrument  line  as  run 
and  the  adjusted  center  line  will  rarely  be  so  great  as  to  require  cor- 
rection for  stationing  of  either  line  from  the  other. 


MONUMENTING   THE   ADJUSTED    CENTER   LlNE. 

Having  projected  the  adjusted  center  line  on  the  adjustment  dia- 
gram and  determined  its  position  from  the  assumed  center  line  by 
offset  distances  at  base-line  points  near  the  ends,  its  angle  with  the 
instrument  line  can  now  be  obtained  and  calculations  made  of  the 
true  curve  connecting  it  with  the  previous  tangent,  with  correct  ad- 
justed stationing  throughout.  The  offset  distance,  therefore,  from 
the  instrument  line  to  the  adjusted  center  line  can  readily  be  ascer- 
tained for  any  station,  and  this  is  essential  for  center-line  monumenting. 

Setting  the  Monuments. — The  adjusted  center  line  should  be  fixed 
on  the  ground  by  stone  monuments  substantially  placed  about  500 
to  800  feet  apart  on  curves  and  1000  to  2000  feet  apart  on  tangents, 
in  order  to  become  readily  convenient  for  use  in  the  field.  They  may 
be  granite,  6  inches  square  on  top  (with  top  dressed  and  i-inch  chisel 
mark  down  the  sides)  and  about  10  inches  square,  rough,  at  the  bottom. 
They  should  be  about  3i  to  4  feet  long  and  set  in  well-tamped  road- 
bed ballast  and  earth,  mixed.  Although  concrete  backing  may  be 
used  if  desirable,  all  soft  places  must  be  strictly  avoided,  as  near  water 
stations,  etc.  The  top  should  be  at  such  an  elevation  that  it  may 
readily  be  found  without  digging,  that  is,  within  view. 

In  setting  monuments  it  has  been  found  convenient  to  locate  the 
monument  station  on  the  base  line,  turn  a  right  angle  and  lay  off  the 
required  distance  to  the  center  line,  fixing  the  point  with  a  tack  in 
stake.  This  point  is  then  carefully  referenced  by  tacks  in  ties,  using 
at  least  one  direct  lateral  and  two  diagonal  measurements. 

After  the  monument  has  been  set  the  exact  center  is  reproduced 
from  the  reference  points  and  marked  by  a  drill-hole  ^  inch  in  diam- 
eter and  %  inch  deep.  The  distances  from  the  center  of  drill-hole  to 
the,  say,  north  and  east  edges  of  the  monument  should  be  recorded. 


BOOKKEEPING  OF  THE  SURVEY.  17 

Finally,  the  monument  should  be  referenced  from  some  prominent 
landmark,  such  as  a  street,  bridge,  or  other  permanent  feature,  so  it 
can  be  readily  found  in  the  future. 

The  Monument  Book. — All  this  information  should  be  recorded 
in  the  monument  book,  which  may  be  an  ordinary  level  book.  It 
should  contain  the  sketches  of  field  operations  previously  prepared 
in  the  office  and  carefully  checked,  also  references  for  setting,  etc. 
The  date  of  setting  should  be  recorded  without  fail;  in  fact  the  dates 
of  all  field  and  of  most  office  operations  should  not  be  neglected. 

THE  LEDGER. 

As  the  survey  progresses  various  classes  of  useful  and  valuable 
data  will  appear  and  these  should  all  be  tabulated  in  the  ledger,  being 
kept  up  to  date  abreast  of  the  journal  as  far  as  practicable.  The 
journal  and  ledger  may  be  kept  up  by  the  field  parties  whenever  field 
operations  slacken,  as  during  bad  weather,  etc. 

The  ledger  may  be  a  cross-section  book  similar  to  the  journal,  and 
special  rulings  made,  as  needed,  for  the  various  tables  of  data. 

The  following  tables  with  column  headings  are  suggested  as 
important: 

A.  New  Alinement  as  per  survey  of (date) showing  also 

new  monuments  set  on  center  line  of  100  feet  right-of-way 

From ....  (place) to (place) (main    or    branch    line) 

R.R. 

1.  Tangent  (or  curve)  No. 

2.  Nearest  depot. 

3.  Approximate  location  (to  street  line,  etc.). 

4.  Map  No.  (new). 

5.  Station  (of  P.C.'s,  P.T.'s,  and  monuments  set). 

6.  Point  (P.C.  or  P.T.). 

7.  Degree  of  curve. 

8.  Tangent  distance  (semi-tang.). 

9.  Intersection  angle  (/). 

10.  True  course  of  tangent. 

11.  Monument  set  (kind). 

12.  Bate  of  setting. 

13.  Elevation,  U.S.C.S.  base. 

14.  Date,  elevation  established. 

15.  Lost  (date). 

1 6.  Reset  (date). 

17.  Remarks. 


1 8  RAILWAY   RIGHT-OF-WAY   SURVEYING. 

Another  table,  very  valuable  for  permanent  record  and  for  making 
the  land  maps,  is  the  following: 

B.  List  of  Monuments  found  and  located  during  survey  of 

(date) ....     From (place) ....  to ....  (place) (main    or 

branch  line) R.R. 

1.  Monument  No. 

2.  Tangent  (or  curve)  No. 

3.  Nearest  depot. 

4.  Approximate  location  (to  street  line,  etc.). 

5.  Map  No.  (new). 

6.  C  Stations  and  ^  Station. 

7.  I  Ranges  from   I  Range  (north). 

8.  i  Established     f  Range  (near  center) . 

9.  I  Center  line     J  Range  (south). 

10.  Kind  of  monument. 

11.  Set  by  whom. 

12.  Date  of  setting  (a = antedates). 

13.  Source  of  information. 

14.  Elevation,  U.S.C.S.  base. 

15.  Date,  elevation  established. 

1 6.  Street  monuments. 

17.  Condition  of  monument. 

18.  (  Correction  {  Station,  +  or  — . 

19.  1  if  righted    f  Range,   +  or  — . 

20.  When  located. 

21.  When  lost  or  destroyed. 

22.  Remarks. 

For  Column  No.  i,  the  monument  number  should  indicate  the 
tangent  on  which  it  is  situated  as  well  as  its  own  relative  position  on 
the  tangent,  as,  for  instance,  monuments  on  Tangent  No.  i  should 
be  numbered  consecutively  101,  102,  103,  etc.,  those  on  Tangent  No.  8, 
801,  802,  803,  etc.  When  tables  are  practically  complete,  if  a  monu- 
ment should  subsequently  be  found  and  located,  the  position  of  which 
on  the  ground  would  place  it  between,  say,  623  and  624,  it  can  be  num- 
bered 623^,  and  so  on. 

If  a  monument  were  adjacent  to  a  curve,  its  range  and  station  would 
be  calculated  with  reference  to  one  or  both  of  the  tangents  produced, 
and  perhaps  also  from  the  center  line  of  the  curve.  Suppose,  for 
illustration,  monument  No.  735  to  be  calculated  with  reference  to 
Tangent  No.  7,  produced  beyond  the  P.C.  of  the  curve  connecting 


BOOKKEEPING   OF  THE   SURVEY.  19 

it  with  Tangent  No.  8.  If  it  were  also  calculated  with  reference  to 
Tangent  No.  8,  its  number  would  remain  735,  but  its  tangent  number, 
in  Column  No.  2,  would  be  8  instead  of  7.  If  it  be  calculated  from 
the  center  line  of  curve  also,  its  tangent  number,  735,  would  still  be 
preserved  for  Column  No.  i,  while  in  Column  No.  2  would  appear 
"Curve  7-8"  or  "Cv.  7-8,"  indicating  that  its  range  and  station 
are  referred  to  the  curve  joining  Tangents  7  and  8.  Hence  a  monu- 
ment situated  on  a  curve  may  require  three  lines  on  the  ledger  sheet, 
one  for  each  tangent  and  one  for  the  curve  itself. 

In  this  connection  it  will  be  well  to  state  that  from  the  ledger  sheet 
the  kind  of  monument  and  its  number  may  be  recorded  in  the  journal, 
adjacent  to  the  monumental  point  of  the  "calculation  sketch"  and  the 
"map  sheet,"  in  blue  ink  on  the  former  and  in  pencil  on  the  latter, 
thus: 

(  \  K=       +1  6^  77  (  TanS-  No-  8+  (Ref-  to  Tan&-  No'  8  Produced 

»     *  3     ^         9-1  V  JT»/~«\ 

5=1531  +  81.62)  beyond  P.C.). 

Stone  M,  No.877  )  Cy  ^  ^    (Ref   tQ  curye  ^   Tang   NQ   g 
*  and  No.  9). 


Stone  M,  No  877  )  to  NQ  duced 

(3)*=       +**MA  backofP.T). 

5=1532  +  31.26; 

Note.—  In  the  case  of  (i)  and  (3)  the  range  is  +,  or  north,  while  for 
(2)  it  is  —  ,  or  south. 

For  "kind  of  monument,"  Column  No.  10,  abbreviations  may  be 
used  as,  for  instance,  "C.I.M."  for  cast-iron  monument,  "I.  Bar" 
for  iron  bar,  "S.M."  or  "Stone"  for  stone  monument,  etc. 

The  "date  of  setting,"  Column  No.  12,  may  be  obtained  from 
office  or  city  records,  or  perhaps  from  the  local  residents.  When  not 
absolutely  sure  of  the  date  a  question  mark  should  accompany  it.  In 
the  case  of  a  monument  being  referred  to  in  deeds  or  other  authentic 
records  as  having  existed  at  a  certain  date  the  letter  (a)  may  be  placed 
before  it  to  indicate  that  the  monument  was  set  prior  to  that  time,  as 
(a)  June,  1867,  means  "antedates  June,  1867." 

For  Column  No.  16,  street  monuments,  the  name  of  the  street  or 
streets  should  be  given,  and  in  the  column  under  "Remarks"  the 
description  of  the  precise  location  with  reference  to  the  centers,  side 
lines,  or  corners  of  the  streets  should  be  noted. 

The  condition  of  the  monument,  Column  No.  17,  is  quite  important 
to  record.  It  may  be  loose,  leaning,  top  broken  off,  good  or  other- 


20  RAILWAY    RIGHT-OF-WAY   SURVEYING. 

wise.  If  it  is  leaning,  as  indicating  a  change  of  position,  the  dip  with 
the  perpendicular  will  be  obtained  in  the  field  and  correction  calcu- 
lated for  "righting"  as  per  Columns  Nos.  18  and  19.  The  correction, 
+  or  — ,  must  be  used  algebraically  with  its  recorded  range  and  station 
to  get  its  presumed  original  position.  The  exception  to  this  rule  will 
be  where  the  range  and  station  of  the  original  position  or  presumed 
original  position  of  the  monument  is  recorded  direct,  in  which  case 
some  note,  as  "Original  position,"  should  accompany  it  in  the  "Re- 
marks" column. 

Column  No.  21,  "when  lost  or  destroyed,"  is  for  future  record. 

The  structural  sheet,  made  up  from  the  right-of-way  survey,  will 
be  invaluable  as  an  aid  to  mapping  and  side-monumenting.  Its  char- 
acteristic feature  is  the  record  of  encroachments. 

C.  List  of  Structures  (fences,  buildings,  bridges,  retaining  walls, 

etc.)  located  during  survey  of ....  (date) 

From (place) to (place) (main  or  branch  line) 

R.R. 

1.  Tangent  (or  curve)  No. 

2.  Nearest  depot. 

3.  Approximate  location. 

4.  Map  No.  (new). 

5.  c  Stations  and  ^  Station. 

6.  j  Ranges  from    I  Range  (north). 

Established      [Range  (near  center). 
Center  line     J  Range  (south). 
9.  Deed  range. 

10.  j  \  On R.R. 

j  Encroachment  c  _ 

11.  (  }  By R.R. 

12.  Kind  of  structure. 

13.  Point  located. 

14.  Built  by  whom. 

15.  When  located. 

1 6.  Condition. 

17.  When  destroyed  or  removed. 

1 8.  When  replaced. 

19.  Remarks. 

Note. — In  Column  No.  9,  "deed  range,"  set  down  the  distance  from 
the  established  center  line  to  the  intended  posit'on  of  the  object  as 
interpreted  from  the  deeds.  Distances  in  Columns  Nos.  10  and  n 
are  simply  the  difference  between  the  actual  range  of  the  structure  and 
the  intended  or  deed  range. 


SIDE-MONUMENTING. 

GENERAL  DISCUSSION. 

SIDE-MONUMENTING  should  be  done  in  connection  with  the  mapping 
with  extreme  care  and  with  legal  advice.  Much  valuable  time  will 
be  lost  and  needless  expense  incurred  if  the  side-monumenting  is  de- 
layed until  the  land  maps  are  otherwise  completed.  Of  course  the 
finished  maps  will  include  the  side  monuments  as  set. 

After  a  side  monument  has  been  set  it  would  be  extremely  difficult 
for  the  company  to  claim  beyond  it  by  moving  "out,"  and  humiliating 
to  retreat;  hence  the  utmost  care  must  be  exercised  in  setting  them. 

Old  records  should  be  carefully  examined,  especially  for  any  dis- 
pute that  may  have  arisen  in  regard  to  the  boundary  line ;  and  if  such 
has  come  up  in  the  past,  it  might  be  wise  to  call  in  the  local  surveyor 
to  adjust  the  line  and  set  the  monuments. 

Information  for  setting  the  side  monuments  should  be  worked  up 
in  the  office  and  taken  into  the  field.  There,  however,  the  practical 
conditions  on  the  ground  may  be  such  as  to  slightly  change  or  com- 
pletely alter  the  office  data  for  laying  out.  In  other  words,  it  may  be 
necessary  to  be  governed  more  or  less  by  conditions  on  the  ground 
rather  than  to  adhere  strictly  to  the  office  notes,  although  the  latter  will 
be  at  least  a  valuable  aid. 

Where  to  Side-monument. — Monuments  should  be  set  as  follows: 

(a)  On  all  important  exterior  jogs,  corners,  and  bends  of  the  right 
of  way. 

(b)  Where  (a)  is  impracticable  owing  to  existing  obstructions,  a 
reference  monument  may  be  set  in  as  serviceable  a  position  as  possible, 
preferably  on  the  right-of-way  line  (sometimes  on  the  land  line)  and 
at  a  certain  recorded  distance  from  the  true  corner  or  bend,  far  enough 
away  so  it  cannot  possibly  be  mistaken  for  the  latter. 

(c)  On  the  right-of-way  lines  opposite  the  P.C.  and  P.T.  of  curves. 

(d)  At  intersection  of  important  land  lines  with  the  right  of  way, 
even  if  there  are  no  jogs  in  the  latter. 

(e)  Frequently  along  right-of-way  lines,  say  opposite  some  of  the 
center-line  monuments  if  other  side  monuments  are  not  close  at  hand. 
This  includes  curves  as  well  as  tangents. 

21 


22  RAILWAY   RIGHT-OF-WAY    SURVEYING. 

(/)  Wherever  there  is  reason  to  fear  encroachment  or  where  it 
already  exists. 

A  table  may  be  prepared  with  the  following  headings  to  meet  ordi- 
nary conditions  for  side-monumenting  and  for  use  in  platting  the  land 
maps.  Part  of  the  data  are  to  be  worked  up  from  office  notes  and 
plans,  and  from  the  ledger  sheets  and  land  maps  as  they  progress. 

D.  Side-monument  Sheet  showing  monuments  set  (and  to  be  set?) 
at  critical  points  on  the  right-of-way  boundary  and  property  lines. 
Survey  of ....  (date) .... 

From (place) to (place) (main  or  branch  line) 

R.R. 

1.  Tangent  (or  curve)  No. 

2.  Nearest  depot. 

3.  Approximate  location. 

4.  Map  No.  (new). 

5.  c  Stations  and  "^  Station. 

6.  J  Ranges  from   !  Range  (north). 


7- 


I    TTofoKKoV,^         I 


Established      f  Range  (near  center) . 


Center  line     J  Range  (south). 
9.  Deed  range  from  new  center  line. 

10.  Angle  between  land  line  and  new  center  line. 

11.  New  station  at  intersection  of  same. 

12.  Kind  of  line. 

13.  Monument  set. 

14.  Date  of  setting. 

15.  When  lost  or  destroyed. 

1 6.  Old  angle  of  land  line  with  old  center  line. 

17.  (  ~.  ,  /  Crossing  old  center  line. 
'     1  Old  stationing  r  ^       .  r 

io.  °  )  Crossing  new  center  line. 

19.  Reference  to  old  notes. 

20.  Deed  range  from  old  center  line. 

21.  Remarks. 


CITY  AND  TOWN  SURVEYS. 

As  the  right-of-way  survey  progresses,  more  or  less  elaborate  city 
and  town  work  is  required.  It  is  a  good  plan  to  locate  every  monu- 
ment in  sight,  wherever  found.  If  the  monuments  located  do  not 
define  the  position  of  the  streets,  the  street  lines  should  be  run  out  and 
connected  with  the  center  line  of  the  railroad,  using  offsets  to  build- 
ings if  they  can  be  obtained  from  the  local  surveyors.  As  a  last  resort 
street  fences  and  curbs  may  be  used  to  fix  the  lines. 

The  amount  of  city  work  to  be  done  will  depend  upon  the  com- 
pany's present  and  prospective  interests  in  the  locality.  All  street 
lines  crossing  the  right  of  way  as  well  as  those  parallel  with  and  a 
short  distance  from  it  should  be  accurately  determined. 

Special  care  should  be  exercised  in  determining  old  as  well  as 
new  street  lines  and  when  the  changes,  if  any,  were  made.  This  matter 
becomes  quite  important  when  it  comes  to  platting  deeds  referring 
to  " street  lines"  on  the  maps. 

Of  course  the  ranges  and  stations  of  all  monuments  located  are 
to  be  calculated  in  the  proper  manner  and  place  in  the  journal  and 
the  results  recorded  in  the  ledger,  sheet  B. 

23 


CONNECTING  WITH  GOVERNMENT  STATIONS. 

FROM  the  table  of  geographical  positions  of  church  spires,  chim- 
neys, flagstaff s,  etc.,  which  have  been  determined  with  accuracy  by 
the  government  and  state  surveys,  many  points  may  be  selected  along 
the  line  of  the  survey  and  located,  generally  by  triangulation. 

The  position,  then,  of  any  point  on  the  survey  can  be  determined 
by  latitude  and  longitude,  and  also  the  true  bearings  of  the  tangents. 
The  latter  is  very  important  in  relation  to  the  magnetic  bearings  of 
the  old  land  lines  where  the  dates  of  same  are  known. 

The  latitudes  and  longitudes  should  be  reduced  to  Clarke's  spheroid 
and  to  the  nearest  hundredth  of  a  second. 

24 


LEVELING. 

IF  it  is  important  to  establish  a  monumented  alinement  on  the 
ground  as  a  backbone  for  future  surveys,  it  is  likewise  desirable  to 
establish  a  system  of  bench-marks  along  the  line  for  convenient  and 
consistent  leveling.  A  good  base  to  adopt  is  that  of  mean  sea-level 
as  established  by  the  U.  S.  Coast  and  Geodetic  Survey.  Equated 
levels  may  be  obtained  with  the  several  city  and  town  bases  along  the 
line  of  the  road. 

ESTABLISHING  BENCH-MARKS. 

In  advance  of  the  leveling,  permanent  benches  should  be  estab- 
lished in  firm  positions  on  masonry  structures  every  half  mile  if  possible. 
A  \"  copper  rivet  with  a  boiler-rivet  head  (flat  at  the  top)  set  into  a 
hole  in  the  masonry  either  by  driving  or  with  cement  makes  a  very 
desirable  and  lasting  bench-mark.  If  provided  with  a  kerf  at  the 
lower  end  and  a  steel  wedge  for  spreading  it  when  driven,  additional 
security  will  result. 

A  good  formula  for  accurate  leveling  of  this  character  is  the  follow- 
ing: ^ 

Error,  up  and  back,  not  to  exceed  .016  ft.V  distance  in  miles,  one  way. 

The  following  system  of  recording  permanent  and  temporary  bench- 
marks, established,  is  recommended  for  the  ledger: 

E.  List  of  Permanent  and  Temporary  Bench-marks  estab- 
lished during  survey  of (date) From (place) to 

(place) (main  or  branch  line) R.R. 

1.  Tangent  (or  curve)  No. 

2.  Nearest  depot. 

3.  Approximate  location. 

4.  Permanent  B.M.  No.  (using  Roman  numerals,  as  I,  II,  etc.). 

5.  Temporary  B.M.  No.  (using  Arabic  numerals,  as  i,  2,  etc.). 

6.  Kind  of  B.M. 

25 


26  RAILWAY   RIGHT-OF-WAY   SURVEYING. 

7.  Station  (new). 

8.  Distance  from  center  line,  N.  or  S 

9.  Description  (accurate). 

10.  Elevation  in  feet,  U.S.C.S.  base. 

11.  Date,  elevation  established. 

12.  When  destroyed. 

13.  Elevation,  south  rail,  Track  No (opposite). 

14.  Reference,  Level  Book. 

15.  Remarks. 

Note. — In  the  column  -of  ''Remarks"  may  be  noted  the  equated 
elevations  of  bench-marks  with  city  bases. 

ELEVATIONS  OF  MONUMENTS. 

From  the  established  bench-marks  the  elevations  of  all  monu- 
ments should  be  obtained  and  recorded  in  the  columns  of  the  ledger 
sheets  as  described  for  that  purpose. 

ELEVATIONS  OF  TRACK  AND  BRIDGES. 

The  elevation  of  the  highest  rail  of  each  track  and  the  clear  head- 
room for  same  at  each  overhead  bridge  or  other  structure  should  be 
ascertained,  and  recorded  on  the  structural  maps. 

PHYSICAL  FEATURES. 

In  connection  with  the  structural  maps,  which  will  be  described 
later,  a  few  of  the  main  physical  features  may  well  [be  shown.  The 
economy  of  having  this  information  in  the  office  might  well  be  illus- 
trated in  the  case  of  a  contemplated  siding.  If  the  structural  maps 
are  made  to  show  the  positions  of  excavations  and  embankments, 
general  ground  elevations,  etc.,  the  superintendent  can  generally 
determine  at  a  glance  whether  the  siding  would  be  practicable,  and 
the  engineer  can  render  an  estimate,  quickly,  without  field  expense. 

Side  Slopes. — The  range,  station,  and  elevation  of  points  of  change 
in  top  and  bottom  of  slopes  should  be  taken,  and  the  character  of  the 
material  noted,  as  far  as  practicable. 

Retaining  Walls. — Range,  station,  and  elevation  of  top  front  and 
bottom  front  of  wall,  depth  of  foundation  (from  office  records,  perhaps), 
and  character  of  wall  should  be  noted. 


or  TMC 
UNIVERSITY 


LEVELING. 


Side  Levels. — These  may  be  taken  to  the  nearest  tenth  of  a  foot, 
to  the  limit  of  the  right  of  way,  or,  in  some  instances,  a  little  beyond. 
The  ordinary  judgment  of  cross-sectioning  will  determine  the  frequency 
and  amount  of  leveling  to  be  done. 


THE  MAPPING. 

THE  mapping  should  begin  immediately  with  the  adjustment  of 
the  first  tangent,  be  carried  on  uninterruptedly,  and  as  it  is  by  far  the 
slowest  and  most  tedious  operation  it  should  be  taken  up  at  various 
advanced  points  along  the  line  as  the  field  work  progresses. 

THE  SCALE. 

Selecting  the  scale  for  the  maps  is  an  important  consideration. 
It  is  largely  dependent  upon  the  requirements  which  the  maps  have 
to  meet;  the  nature,  extent,  and  system  of  existing  records;  also  the 
accuracy  of  proposed  survey.  The  latter  will  be  assumed  to  be  in 
accordance  with  the  methods  herein  described. 

The  usual  scale  is  100,  and  this  may  be  used  for  outlying  sections, 
simple  in  character,  and  where  company  property  extends  considerably 
beyond  the  right  of  way.  It  will  be  found,  however,  that  a  scale  of 
50  is  none  too  large  for  maps  embracing  strictly  railroad  properties 
in  populated  districts,  with  many  and  complicated  land  lines,  monu- 
ments, etc.,  to  register.  With  some  roads  which  have  acquired  their 
right  of  way  in  piecemeal,  as,  for  instance,  25-  or  33-ft.  strips,  widened 
to  50  or  66  feet,  and  again  later  to  100,  with  one  or  more  old  center 
lines,  it  would  be  necessary  to  use  a  5o-ft.  scale. 

In  the  case  of  terminals,  etc.,  where  both  conditions  exist,  it  is 
sometimes  desirable  to  use  both  scales,  making  two  sets  of  maps. 

LAND  AND  STRUCTURAL  MAPS  COMPARED. 

The  land  and  the  structural  maps  should,  generally,  be  separate, 
but  have  similar  numbers  and  embrace  similar  areas. 

The  land  maps  may  include  such  structural  features  as  will  explain 
more  clearly  certain  agreements,  as,  for  instance,  the  allowed  encroach- 
ments of  abutments  or  other  structures  within  the  right  of  way,  etc. 

On  the  other  hand,  the  structural  maps  should  show,  in  addition 
to  the  structural  and  physical  features,  the  exact  position  of  the  com- 
pany's exterior  boundary  lines,  accurately  defined  so  they  can  be  pro- 
duced on  the  ground. 

28 


THE   MAPPING.  29 


THE  LAND  MAPS. 

The  Paper.— The  original  land  maps  should  be  on  durable  mounted 
white  paper  of  close  texture  and  character  which  will  stand  erasing, 
and  not  fade  too  much  under  ordinary  light.  The  best  is  none  too 
good. 

When  finished  to  date  they  may  be  bound  in  book  form,  or  remain 
as  loose  sheets  and  filed  in  shallow,  removable,  sheet-steel  or  light 
wooden  drawers  with  "drop  sides." 

They  should  be  kept  up  to  date  from  records  filed  with  the  Real 
Estate  Department. 

A  set  of  tracings  may  be  made  for  the  Law  Department  and  kept 
up  to  date  in  a  similar  manner,  but  promiscuous  blue-printing  should 
be  avoided. 

Laying  out  the  Map. — Having  selected  the  scale,  say  50,  and  the 
size  of  the  map,  say  28"X42"  inside  of  border  (sheet  29//X43//), 
bisect  the  sheet  longitudinally  by  a  base  line  and  lay  off  the  border 
line  very  accurately.  This  base  line  becomes,  generally,  the  adjusted 
center  line  of  the  tangent  or  tangent  produced,  as  the  case  may  be. 
It  should  be  drawn  in  red  (carmine)  ink  and  the  stationing  laid  off, 
with  red  circles  every  fifth  station,  at  the  "5"  and  "10"  points,  unless 
a  stone  monument  has  been  set  there,  in  which  case  it  would  have  the 
" stone  monument"  symbol,  a  square  outline  in  black. 

It  is  well  to  project  "5oo-ft. "  range  and  station  lines  outside  the 
border,  thus  blocking  the  map  off  in  5oo-ft.  squares,  virtually  pre- 
serving the  scale.  The  5oo-ft.  stationing  may  also  be  noted  on  these 
lines  at  the  top  of  the  sheet. 

Platting. — From  the  journal,  ledger,  abstracts  of  deeds,  old  plans, 
etc.,  the  maps  are  constructed.  The  field-survey  notes,  worked  up 
in  the  journal  and  ledger,  will  show  the  true  positions  of  all  streets 
and  street  rhonuments  in  the  vicinity  of  the  railroad,  all  important 
structures  which  may  have  a  bearing  in  determining  the  positions  of 
land  lines,  and  any  monuments  previously  set  along  the  right  of  way. 

With  these  practical  data  which  have  been  reduced  to  rectangular 
coordinates  for  simplified  position  the  deeds  may  readily  be  located 
and  platted  on  the  maps. 

The  platting  should  be  as  accurate  as  possible  and  not  a  mere 
picture  map  with  wide  shaded  street  lines,  etc.  Lines  should  be  shown 
firm  and  clear  but  not  heavy.  It  is  a  good  rule  to  show  the  present 


30  RAILWAY    RIGHT-OF-WAY   SURVEYING. 

right-of-way  lines,  or  rather  outer  boundaries,  in  full,  and  the  numerous 
interior  lines  due  to  piecemeal  purchases,  etc.,  dotted.  If  some  of  the 
latter  are  more  important  than  others,  heavier  or  longer  dots  may  be 
used. 

Vacated  streets  should  be  shown  dotted,  but  perhaps  the  center 
line  of  the  street  in  full  if  it  form  an  important  land  line.  In  cases 
of  abandoned  streets  the  original  abutting  owners  may  justly  claim 
to  the  center  line  (with  right-angle  side  lines)  by  reversion.  It  is  very 
difficult  in  many  cases  to  interpret  both  legally  and  practically,  but 
recourse  can  always  be  had  to  the  Law  Department,  and  in  fact  the 
whole  work  should  be  done  in  very  close  touch  therewith,  as  many  legal 
questions  arise  in  settling  land  lines,  side-monumenting,  etc. 

Old  and  New  Center  Lines. — If  there  be  an  old  center  line,  its 
position  will  be  revealed  by  the  platting.  It  may  or  may  not  be  identi- 
cal with  the  recently  adjusted  center  line. 

If  the  two  are  identical,  the  new  stationing  may  be  on  one  side  of 
the  line,  say  the  upper,  and  the  old  stationing  on  the  other,  the  lower. 
On  the  lower  side  of  the  line,  then,  reference  will  be  made  to  the  old 
center  line,  giving  date  of  filing,  magnetic  bearing,  etc.  On  the  upper 
side  of  the  line  will  be  recorded  notes  regarding  the  adjusted  center 
line,  with  date  of  same,  also  the  "true  bearing"  to  the  nearest  one 
quarter  minute.  The  true  bearing  may  be  obtained  by  solar  work 
or  from  the  survey  connecting  the  government  and  state  triangulation 
stations. 

If  the  old  center  line  be  not  identical  with  the  new,  it  can  be  shown 
in  vermilion  ink  as  distinguishing  it  from  the  adjusted  (in  carmine), 
and  each  designated  line  titled  separately.  If  it  were,  say,  the  center 
of  a  former  66-ft.  right  of  way  and  subsequently  an  additional  strip 
(34  feet)  were  purchased  on  one  side,  making  the  present  right  of  way 
100  feet,  the  two  center  lines  would  be  shown. 

Another  case  to  be  met  with  is  where  the  old  filed  center  line  was 
found  to  be  sinuous  in  years  back,  and  an  attempt  was  made  to  straighten 
it  at  the  time  of  acquiring  additional  right  of  way.  The  present  re- 
adjustment will,  of  course,  attempt  to  follow  closely  the  "straightened" 
line  even  if  a  "bend"  is  found  necessary  in  the  "tangent." 

Subsequent  to  the  "straightening"  some  of  the  deeds,  perhaps 
intentionally,  may  refer  to  it  as  the  filed  line.  This  will  doubtless 
cause  some  confusion  in  addition  to  that  arising  from  other  quarters, 
such  as  deeds  giving  wrong  bearings,  scaled  distances  using  the  wrong 
scale,  etc.  These  problems  can  usually  be  solved  with  care. 


THE  MAPPING.  3  1 

Symbols.  —  Recognized  symbols  may  be  used  as  follows: 

O  =  iron  monument  ; 

O  with  the  particular  name  after  it  may  be  used  to  designate  any  kind 

of  monument. 
D  =  stone  monument. 

The  ranges  and  stations  of  all  monuments  should  be  shown  with 
reference  to  the  adjusted  tangent  if  they  are  on  the  tangent.  If  the 
monument  is  adjacent  to  a  curve,  its  range  and  station  will  be  shown 
with  reference  to  the  curve  and  to  one  or  both  of  the  tangents  produced. 

For  illustration, 

C.I.M. 


j  *=  +  49.96       iTang.No.8+ 
(5=123+13.44) 


means,  "Cast-iron  monument,  range  north  49.96  from  station  123+  13.44 
referred  to  Tangent  No.  8  produced  toward  No.  9."  Likewise,  "Tang. 
No.  8—,"  after  the  bracket,  would  mean,  "Tangent  No.  8,  produced 
toward  No.  7,"  while  the  absence  of  the  algebraic  sign  altogether  would 
signify,  simply,  "Tangent  No.  8,"  itself.  The  plus  sign  before  the 
range  indicates  "north,"  and  the  minus  sign  "south." 
Again, 

•n  £• 

\  Cv.  Nos.  8—Q 
5=123+13.44) 

means,  "  Stone  monument,  range  south  49.96  from  station  123+  13.44 
referred  to  curve  connecting  Tangents  Nos.  8  and  9." 

Generally  the  absence  of  "Cv "  after  the  bracket  will  signify 

that  the  range  and  station  are  referred  to  the  tangent  or  tangent  pro- 
duced. 

Index  to  Transfers. — The  various  transfers  are  shown  on  the  lots 
by  numbers  in  red  ink  inside  of  red  circles,  or  if  the  lot  is  very  small 
the  circle  may  be  omitted. 

An  index,  or  list  of  transfers,  is  shown  on  each  land  map  in  a  per- 
manently vacant  space  where  it  will  not  interfere  with  the  map  proper, 
and  each  transfer  is  recorded  under  the  following  headings: 

1.  Office  File  (as  "Essex  36" — Essex  County,  deed  No.  36). 

("Essex  36"  in  red  for  purchases  and  green  for  sales.) 

2.  Grantor. 

3.  Grantee. 

4.  Map  No.  (of  lot),  as  1360,  1366,  etc. 


32  RAILWAY    RIGHT-OF-WAY   SURVEYING. 

5.  Date  (of  deed). 

6.  Conveyance  (as  W= warranty,  Q.C.  =  quitclaim,  etc.). 

7.  Record  Book  (in  office). 

8.  Page  (of  Record  Book). 

9.  Remarks  (special  clauses  and  agreements). 

Property  Lines. — A  narrow  thin  liquid  carmine  shading  along  the 
outline  of  the  company  property  shows  clearly  present  ownership^ 
while  a  liquid  green  shading  shows  property  formerly  owned  by  the 
company.  As  transfers  take  place  the  new  coloring  can  be  put  on, 
even  over  the  old,  and  the  maps  kept  up  to  date. 

Some  theoretical  objection  may  be  made  to  this  method,  but  it  can 
be  truly  stated  that  the  new  coloring  shows  quite  clearly,  and  that 
maps  are  in  existence  which  have  been  kept  up  for  thirty-five  years 
in  this  manner,  through  periods  of  numerous  land  transfers,  both 
buying  and  selling,  and  clearly  show  the  properties.  They  are  the 
main  record  to-day. 

The  conventional •  may  be  used  if  preferred.  Much 

will  depend  upon  local  conditions. 

North  Point. — The  north  point  should  be  in  some  obscure  part 
of  the  sheet  free  from  interference  with  present  or  future  matter.  It 
should  be  the  "true"  north  and  so  marked. 

Explanatory  Notes. — Near  the  north  point  in  all  cases  should  be 
the  special  or  explanatory  notes  for  stationing,  monuments,  coloring, 
true  bearing,  etc. 

Title. — The  title  of  the  map  should  be  outside  the  border  line, 
part  above  the  upper  and  part  below  the  lower,  along  the  J-inch  mar- 
gins at  the  right  hand  of  the  sheet.  For  instance,  at  the  top  of  the 
map  may  be  the  name  of  the  road,  main  line  or  branch  and  sheet  num- 
ber, while  at  the  bottom  may  be  the  general  title  of  the  adjustment 
survey,  scale,  date,  and  sheet  number  repeated. 

A  Base  for  the  Structural  Maps. — Besides  serving  their  regular 
purpose  in  the  land  office  these  maps  constitute  a  base  for  the  struc- 
tural maps,  which  should  closely  follow  and  which  will  now  be  ex- 
plained. 

THE  STRUCTURAL  MAPS. 

The  structural  maps  will  embrace  considerable  information  from 
the  land  maps,  together  with  the  structural  and  certain  physical  fea- 
tures along  the  line. 


THE   MAPPING.  33 

From  the  Land  Maps. — In  direct  contrast  with  the  land  maps,  the 
structural  maps  should  be  on  tracing  cloth  for  the  purpose  of  furnish- 
ing blue-prints  when  required.  Generally  they  should  be  to  the 
same  scale  as  the  land  maps,  and  from  the  latter  may  be  traced 
directly  the  adjusted  center  line,  center-line  monuments,  side  lines, 
side-line  monuments,  intersecting  land  lines,  streets,  etc.  They  need 
show  only  the  "outline"  of  present  ownership  and  not  the  "built- 
up"  right  of  way  as  it  appears  on  the  land  maps. 

The  side  lines  may  be  correctly  exhibited  by  showing  the  positions 
of  "points  of  bends"  by  ranges  and  stations  from  the  center  line,  also 
the  angles  at  these  bends  and  the  lengths  of  side  lines,  where  advisable. 

The  alinement  will  be  that  of  the  adjusted  center  line  as  monu- 
mented. 

Company  property  lines  may  be  shown  on  the  tracings  by  the  stand- 
ard dash,  dot,  dot,  dash,  dot,  dot,  etc.,  somewhat  heavier  than  the  dash, 
dot,  dash,  dot  used  to  represent  fences.  A  fine  red  crayon  shading 
may  also  be  carried  around  inside  of  these  lines  if  desirable  to  bring 
out  more  clearly  the  company  property. 

Structural  Features. — On  these  maps  should  be  shown  all  tracks, 
bridges,  abutments,  culverts,  buildings,  fences,  signals,  etc.,  in  fact 
all  structural  features.  They  must  be  drawn  carefully  to  scale,  and 
furthermore  the  ranges  and  stations  recorded  for  all  important  or 
critical  points,  as  fence  or  building  corners,  frog-points,  etc.  In  cases 
of  long  stretches  of  track  or  side  fences,  apparently  straight,  the  ranges 
only  need  be  shown  opposite  "round  stations"  on  the  center  line. 

Economic  Method. — It  would  be  a  waste  of  time,  involving  needless 
expense,  to  start  out  in  the  field  and  measure  up  everything  regardless 
of  hundreds  of  existing  surveys  and  plans  in  the  office  of  the  company 
which  can  be  utilized  by  "tying  them  in"  carefully  to  the  monumented 
center  line.  Although  not  strictly  modern,  they  will,  many  of  them, 
answer  the  purpose  temporarily,  to  be  supplanted  later  with  informa- 
tion of  a  more  definite  character  during  the  ordinary  course  of  work, 
without  added  expense.  Judgment  must  be  used  as  to  whether  entirely 
new  surveys  are  essential  in  certain  localities. 

Maps  compiled  from  office  records,  or  from  new  surveys,  should 
so  be  designated. 

Whenever  new  surveys  are  made  or  changes  occur  in  location  of 
track  or  structures  of  any  kind,  tracing  plans  of  such  changes  will 
be  made.  These  should  become  identified  with  the  structural  maps 
of  the  particular  localities  and  blue-prints  of  same,  or  at  least  memo- 


34  RAILWAY   RIGHT-OF-WAY   SURVEYING. 

randa,  filed  therewith.  In  this  way  small  changes  and  additional 
information  may  be  kept  track  of,  and  after  a  certain  length  of  time, 
or  when  a  sufficient  number  of  changes  have  taken  place,  new  struc- 
tural tracings  may  be  made  embracing  all  changes  to  date.  Blue- 
prints of  these  tracings  should  be  sent  out  to  supersede  all  previous 
prints  furnished,  which  will  be  filed  away  as  matter  of  record  or  history. 

Physical  Features. — Contour  lines  cannot  well  be  shown,  but  the 
edges  of  slopes  in  excavation  and  embankment  may  be  outlined,  with 
elevations  along  same  at  intervals,  and  also  beyond  to  limit  of  right 
of  way. 

Elevations  of  top  of  rail,  top  and  bottom  of  retaining  walls,  bridge 
seats,  depot  platforms,  etc.,  will  suggest  themselves  as  important  data 
for  the  maps.  The  clear  head-room  at  each  crossing  referred  to  actual 
elevations  from  the  adopted  base  will  be  most  convenient. 

THE  INDEX  MAPS. 

For  ready  reference  to  the  land  and  structural  maps  the  index  maps 
are  prepared,  platted  on  a  true  polyconic  projection,  using  Clarke's 
spheroid. 

Adopting  a  scale  of  4000  feet  to  the  inch,  the  parallels  of  latitude 
may  be  shown  every  two  minutes  and  the  meridian  lines  2^  minutes 
apart. 

The  government  triangulation  stations,  which  have  been  located 
by  the  survey  with  a  view  to  adjusting  the  alinement  on  the  maps,  are 
platted  by  latitude  and  longitude. 

The  Alinement. — The  alinement  and  triangulation  stations  are 
platted  on  tracing  cloth  by  the  survey  notes,  matched  on  the  index 
map  by  these  stations,  and  the  alinement  produced  thereon  in  its  proper 
geographical  position. 

Along  the  center  line  as  platted  are  shown  the  stationing,  every 
1000  feet,  the  names  of  depots,  and  the  outline  position  of  each  land 
or  structural  map  to  scale,  with  map  number  of  same  in  red. 

True  Bearings. — The  true  bearings  of  tangents  may  be  obtained 
in  the  following  manner: 

a.  Calculate  the  true  bearing  of  the  imaginary  line  joining  two 
important  government  stations,  situated  some  distance  apart  and 
which  have  been  located  by  the  survey,  using  the  latitudes  and  longi- 
tudes of  the  stations,  reducing  the  differences  to  feet,  and  solving  the 
triangle  as  a  right-angle  triangle.  The  angle  obtained  will  give  the 


THE  MAPPING.  35 

true  divergence  of  the  line  from  the  meridian  passing  through  its  middle 
point. 

b.  Project  this  meridian  on  the  map  and  note,  by  scale,  the  station 
where  it  intersects  the  center  line. 

c.  The  angles  worked  up  from  the  survey  traverse,  in  connection 
with  the  true  bearing  of  the  line  joining  the  government  stations,  as 
above,  will  point  to  the  true  bearing  of  the  tangent  at  its  station  of 
intersection  with  said  meridian. 

As  meridians  converge  toward  the  north,  it  is  evident  that  for  any 
tangent  running  easterly  and  westerly  its  true  bearing  will  vary  at 
different  points  on  the  tangent.  For  instance,  on  an  east-and-west 
line  in  the  latitude  of  New  York  there  is  a  variation  of  about  one  second 
in  bearing  at  points  117  feet  apart,  or  one  minute  in  about  ij  miles. 
The  distance  apart  of  points  on  any  line  in  this  latitude  for  a  variation 
in  bearing  of  one  second  will  consequently  be  1 17  X  cosecant  of  true 
bearing  angle  of  line  with  the  meridian. 

In  this  manner,  considering  the  average  latitude  or  calculating 
for  different  average  latitudes,  as  the  case  may  demand,  the  true  bear- 
ings may  be  obtained  to  the  second  for  any  tangent  at  any  point.  They 
should  be  calculated  at  every  stone  monument  and  recorded  in  Column 
No.  TO  of  the  alinement  sheet. 


APPENDIX. 


HINTS  FOR  FIELD  WORK. 

TABLE  OF  TEMPERATURE  CORRECTIONS. 

TABLE  OF  ALLOWABLE  ERRORS  IN  LEVELING. 

TABLE  OF  NATURAL  TANGENTS  AND  COTANGENTS  FOR  PLATTING. 

TABLE  OF  FEET  AND  CHAINS. 

TRIGONOMETRIC  FORMULAS. 

37 


APPENDIX. 

HINTS  FOR  FIELD  WORK. 

IT  might  not  be  out  of  place  here  to  speak  of  some  apparently 
simple  matters  (but  in  reality  far-reaching)  in  connection  with  work 
on  the  line. 

As  men  are  greatly  separated  at  times,  or  ordered  beyond  speaking 
distance  (this  in  the  truly  literal  sense)  to  perform  certain  harmonious 
duties,  they  must  keep  wide  awake.  Codes  of  signals  will  be  adopted, 
but  they  should  be  simple  and  few.  Men  will  learn  to  understand 
each  other  as  they  become  drilled  to  the  work. 

Cheap  men  are  not  economical.  They  are  an  encumbrance  and 
liable  by  serious  errors  to  render  the  work  not  only  expensive  but 
questionable. 

The  assistant  in  charge  of  the  field  party  should  take  the  notes, 
keep  his  eyes  open,  and  not  be  obliged  to  run  the  instrument. 

In  chaining,  the  hind  chainman  should  hold  the  zero  end  of  the 
tape  constantly  on  the  point  while  the  head  chainman  is  taking  the 
reading.  As  the  tape  cannot  be  held  absolutely  fixed  in  position  con- 
tinuously, the  hind  chainman  should,  when  he  thinks  the  head  chain- 
man is  ready,  call  sharply  "right,"  " right,"  at  frequent  intervals. 
The  head  chain  takes  the  reading  or  readings  at  such  instants,  and  if 
they  are  satisfactory  he  answers  "all  right."  If  the  hind  chain  is 
slow,  careless,  and  awkward,  many  errors  will  result.  A  good  custom 
is  for  the  head  chainman  to  read  the  foot-mark  beyond  the  true  measure- 
ment, as  well  as  the  one  before  it,  as  a  check. 

Constant  attention  to  the  work  at  hand  will  secure  not  only  rapid 
but  accurate  results,  and  they  cannot  be  secured  otherwise. 

TABLE  OF  TEMPERATURE  CORRECTIONS. 

Assuming  the  coefficient  of  expansion  for  tape-steel  to  be  .ooooo6f 
per  degree  Fahrenheit,  there  would  be  a  change  of  .01  feet  in  a  loo-foot 
tape  for  each  15  degrees  variation  in  temperature. 

39 


RAILWAY   RIGHT-OF-WAY   SURVEYING. 


The  following  table  shows  corrections  in  decimals  of  a  foot  per 
100  feet  (for  tapes  standard  at  40°  to  85°)  to  be  applied  to  measure- 
ments taken  at  temperatures  varying  from  o°  to  100°  F.  For  instance, 
if  the  tape  be  standard  at  60°  and  the  measurement  taken  at  20°,  the 
correct  measurement  would  be  .027  foot  less  per  100  feet. 

TABLE. 


loo-foot  Tape  Standard  at  following  Temperatures. 

40° 

45° 

5°° 

55° 

60° 

65° 

70° 

75° 

80° 

85° 

o° 

—  .027 

—  -03 

—  -033 

-  -037 

—  .04 

—  -043 

—  .047 

-  -05 

-  .053 

-.057          o° 

5° 

—  .023 

—  .027 

-  -03 

-.033 

—  -037 

—  .04 

-  -043 

—  .047 

-  -05 

-.053,         5° 

10 

—  .02 

—  .023 

—  .027 

-  -03 

—  -033 

-  -037 

-  .04 

-.043 

-  .047 

-  -05 

10° 

15° 

-  .017 

—  .  02 

—  .023 

—  .  027 

-  -03 

-  -033 

—  -037 

-  .04 

-  .043 

-.047 

15° 

20 

-  .013 

—  .017 

—  .02 

—  .023 

—  .027 

-  -03 

-  -033 

-  -037 

-  .04 

—  -043 

20° 

25U 

—  .01 

—  .013 

—  .017 

—  .02 

—  .023 

—  .027 

-  -03 

—  -033 

-  -037 

-.04 

25° 

30° 

—  .007 

—  .01 

-.013 

—  .017 

—  .02 

—  .023 

—  .027 

—  -03 

-  .033 

—  -037 

30° 

1 

35° 

—  .003 

—  .  007 

—  .  or 

—  .013 

—  .017 

—  .02 

—  .023 

-  .027 

-  -03 

-•033 

35° 

3 

40° 

— 

—  .003 

—  .007 

—  .01 

—  .013 

—  .017 

—  .02 

—  .023 

—  .  027 

-  -03 

40° 

i 

45° 

+  .003 



—  .003 

—  .007 

—  .01 

—  .OI3 

—  .017 

—  .02 

—  .023 

—  .027 

45° 

a 

50" 

+  .007 

+  .003 

— 

-  .003 

-  .007 

—  .OI 

—  .013 

-  .017 

—  .02 

—  .023 

50° 

E 

V 

55° 

+  .01 

+  .007 

+  -003 

-  .003 

—  .007 

—  .01 

-.013 

—  .017 

—  .02 

55° 

"3 

60° 

+  .013 

+  .01 

+  .007 

+  .003 



—  .003 

-  .007 

—  .  01 

-   .013 

—  .017 

60° 

T 

65° 

+  .017 

+  .013 

+  .01 

+  .007 

+  .003 

-  .003 

—  .007 

—  .OI 

-  .013 

65° 

&H 

70° 

+  .02 

+  .017 

+  .013 

+  .01 

+  .  007 

+  -003 

-  .003 

—  .007 

—  .01 

70° 

75° 

+  -023 

+  .02 

+  .017 

+  .013 

+  .01 

+  .007 

+  -003 



-  .003 

-  .007 

7S° 

80° 

+  .  O27 

+  .023 

+  .02 

+  .017 

+  .013 

+  .01 

+  .  007 

+  -003 

—  .  003 

80° 

85° 

+  .03 

+  .027 

+  -023 

+  .02 

+  .017 

+  .013 

+  .or 

+  .007 

+  -003 

85° 

90° 

+  -033 

+  .03 

+  .027 

+  .023 

+  .02 

+  .017 

+  .013 

+  .01 

+  .  OO7 

+  .003 

90° 

Q5° 

+  .037 

+  -033 

+  .03 

+  .027 

+  -023 

+  .02 

+  .017 

+  .013 

+  .01 

+  .007 

05° 

100° 

+  .04 

+  -037 

+  -033 

+  .03 

+  .027 

+  -023 

+  .02 

+  .017 

+  .013 

+  .01 

IOO° 

The  above  signs,  +  and  — ,  are  to  be  adhered  to  in  making  tem- 
perature corrections  for  measurements  between  fixed  objects  in  the 
field.  That  is,  if  the  actual  temperature  when  the  measurement  is 
taken  is  below  the  tape  standard  temperature,  the  correct  distance  is 
less  than  the  tape  reading  and  hence  the  correction  is  minus.  For 
an  actual  temperature  above  that  of  the  tape  standard  the  correction 
is  plus. 

For  laying  out  certain  distances  (as  in  staking  out  monuments)  on 
the  ground,  the  apparently  reverse  operation  holds  true.  If  the  actual 
temperature  is  below  that  of  the  tape  standard,  the  temperature  cor- 
rection should  be  added,  and  if  above,  subtracted. 


APPENDIX. 


TABLE   OF  ALLOWABLE   ERRORS   IN    LEVELING. 


Distance, 
Miles. 

Distance, 
Feet. 

Allowable 
Error.* 

Distance, 
Miles. 

Distance, 
Feet. 

Allowable 
Error.* 

.  I 

528 

.005 

.0189 

100 

.0022 

•I25 

660 

.006 

.04 

200 

.003 

•25 

1320 

.008 

.06 

300 

.004 

•333 

1760 

.009 

.08 

4OO 

.004 

•  5 

2640 

.Oil 

.09 

500 

.005 

.625 

3300 

.013 

.  II 

600 

.005 

•75 

3960 

.014 

•13 

700 

.006 

i 

5280 

.016 

•is 

800 

.006 

1.25 

6600 

.018 

•  17 

9OO 

.007 

i-5 

7Q20 

.020 

.19 

1000 

.007 

i-75 

9240 

.021 

•23 

1200 

.008 

2 

10560 

.023 

.27 

1400 

.008 

2-5 

13200 

.025 

•30 

I6OO 

.009 

3 

15840 

.028 

.38 

2000 

.010 

4 

2II20 

.032 

•47 

2500 

.Oil 

5 

26400 

.036 

•57 

3000 

.012 

6 

31680 

•  039 

.66 

35°° 

•013 

8 

42240 

•045 

.76 

4000 

.014 

10 

52800 

.051 

•85 

4500 

.015 

12 

63360 

•055 

•95 

5  coo 

.Ol6 

15 

79200 

.062 

1.14 

6000 

.017 

20 

105600 

.072 

r-33 

7000 

.018 

25 

132000 

.080 

1-52 

8000 

.O2O 

30 

158400 

.088 

'1.70 

9000 

.021 

40 

2II200 

.  IOI 

1.89 

1  0000 

.022 

50 

264000 

•  113 

2.08 

1  1  000 

.023 

60 

316800 

.124 

2.27 

12000 

.024 

70 

369600 

.134 

2.46 

13000 

.02" 

80 

422400 

•  143 

2.65 

14000 

.026 

QO 

475200 

.152 

2.84 

15000 

.027 

lOo 

52800O 

.160 

3-03 

16000 

.028 

125 

660000 

.179 

3.22 

17000 

.029 

15° 

792000 

.196 

3-4i 

18000 

.030 

175 

924000 

.  212 

3-79 

20000 

.031 

2OO 

1056000 

.226 

4.17 

22000 

•033 

250 

I32OOOO 

•253 

4-73 

25OOO 

•°35 

300 

1584000 

.277 

5.68 

30000 

.038 

350 

1848000 

.299 

6.63 

35000 

.041 

400 

2II200O 

•320 

7-58 

40000 

.044 

45° 

2376000 

•339 

8.52 

45000 

.047 

500 

2640000 

-358 

9-47 

50000 

.049 

Error  (in  feet)  leveling  "up  and  back"  must  not  exceed 

.oi6Vdistance  in  miles  (one  way). 


RAILWAY   RIGHT-OF-WAY   SURVEYING. 


TABLE  OF  NATURAL  TANGENTS  AND 


Diff. 

for  i'. 

Tan- 
gents. 

o' 

5' 

10' 

15' 

•20' 

25' 

30' 

2.9 
2.9 
2.9 
2.9 
2.9 

0° 

1° 

2° 

3° 
4° 

.0000 

•OI75 
•0349 
.0524 
.0699 

.0015 
.0189 
•  0364 

•°539 
.0714 

.0029 
.0204 

.0378 

•°553 
.0729 

.0044 
.0218 

•  0393 
.0568 

•°743 

.0058 
•0233 
.0407 
.0^82 
'  .07*8 

.0073 
.0247 
.0422 

•°597 

.0772 

.0087 
.0262 

•°437 
.0612 
.0787 

89° 
88° 
87° 
86° 
85° 

2.9 
2.9 
3- 
3- 
3- 

5 
6° 

7° 
8° 
Q° 

.0875 
.  10^1 
.1228 
.1405 
.1584 

.0890 
.1066 
.1243 
.  1420 
•1599 

.0904 
•.1080 

•1257 

•  U35 
.  1614 

.0919 
.1095 
.1272 

•  145° 
.  1629 

•0934 

.  IIIO 

.1287 

•  1465 
.1644 

.0948 
.1125 
•  I3°2 
.  1480 

.1658 

.0963 
•JI39 
•I3i7 
•I495 
•  1673 

84° 

83° 
82° 
81° 
80° 

3- 
3- 
3- 
3- 

10° 

n° 

12° 
13° 

14° 

.1763 

.1944 

.2126 
.2309 

•  2493 

.1778 

•1959 

.2141 
.2324 
•  2509 

•J793 
.1974 
.2156 

•2339 
.2524 

.1808 
.1989 
.2171 

•2355 
.2540 

•  l823 
.2004 
.2186 
.2370 

•2555 

.1838 

.2019 

.2202 

•2385 

.  2C7I 

•  1853 
2035 
.2217 
.2401 
•2586 

79° 

78° 

77° 
76° 

75° 

3- 
3- 
3- 
3- 
3-3 

15° 

i6°" 
17° 
18° 
19° 

.2679 
.2867 

•3°57 
•3249 
•  3443 

.2695 
.2883 

•3073 
•3265 
-  3460 

.2711 
.2899 
.3089 
.3281 
.  3476 

.2726 

•2915 
•3IOS 
.3298 

•3492 

.2742 
.2931 
.3121 
•33J4 
•  35o8 

•2758 

.2946 

•  3137 

•333° 
•3525 

•2773 
.2962 

•3153 
•3346 
•3541 

74° 
73° 
72° 
7i° 
70° 

3-3 
3-4 
3-4 
3-4 
3-5 

20° 
21° 
22° 
23° 

24° 

.3640 

•3839 

.  4040 

•4245 
•4452 

•3656 
•3855 
•4057 
.4262 
.4470 

•3673 
.3872 
.4074 
.4279 
•4487 

.3689 
.3889 
.4091 
.4296 
•  4505 

•  37o6 
•  3906 
.4108 

•4314 
.4522 

.3722 
.3922 
•4125 
•4331 

•  4540 

•  3739 
•  3939 
.4142 

•4348 

•4557 

69° 
68° 
67° 
66° 
65° 

3-6 
3-6 
3-7 
3-8 
3-8 

25° 
26° 
27° 
28° 
29° 

.4663 

.4877 
•  5°95 
•53i7 
•5543 

.4681 

•4895 
.5114 

•5336 
.5562 

.4699 

•4913 

•5J32 
•5354 
•558i 

.4716 
•4931 
•S^S0 
•5373 
.5600 

•4734 
•  495° 
.5169 

•53Q2 
.5619 

•4752 
.4968 
•5187 
•5411 
•5639 

.4770 
.4986 
.5206 

•  543° 
•5658 

64° 

63° 
62° 
61° 

60° 

3-9 

4.0 
4-  i 

4.  2 

4-3 

30° 
31° 

32° 

33° 
34° 

•5774 
.6009 
.6249 
.6494 
.674^ 

•5793 
.6028 
.6269 
•6515 
.6766 

.5812 
.  6048 
.6289 
•  6536 

.6787 

•  5832 
.6068 
.6^10 
.6556 
.6809 

.5851 

.  6088 
•  6330 
•6577 
.  6830 

•  5871 
.6108 
•6350 
.6^98 
.6851 

.^890 
.6128 

•6371 
.6619 
.6873 

59° 

S8° 

57° 
56° 

55° 

4-4 
4-5 
4.6 
4-7 
4.9 

35° 
36° 

37° 
38° 
3Q° 

.7002 
.7265 
•  7536 
•7813 
.8098 

.7024 
.7288 
.7558 
.7836 
.8122 

.7046 

•7310 
.7581 
.7860 
.8146 

.  7067 

•  7332 
.7604 
.7883 
.8170 

.  7089 

•  7355 
.7627 
.7907 
.8195 

.7111 

•7377 
•  7650 
•7931 
.8219 

•7i33 
.7400 

•  7673 
•  7954 
.8243 

54° 
53° 
52° 
5i° 

50° 

S-o 
5-1 
5-3 
5-5 

5-7 

40° 
4i° 
42° 
43° 
44° 

.8391 
.8693 
.9004 
•9325 
•9657 

.8416 
.8718 
•  9°3° 
•9352 
.9685 

.8441 
.8744 

•9057 
.9380 

•9713 

.8466 
.8770 
.9083 
.9407 
.9742 

.8491 
.8796 
.9110 

•  9435 
.9770 

.8516 

.8821 

•9*37 
.9462 

.9798 

.8^41 

.8847 
.9163 
.9490 
.9827 

49° 

48° 

47° 
46° 

45° 

60' 

55' 

50' 

45' 

40' 

35' 

30' 

Cotan- 
gents. 

Example.  —  To  plat  angle  33°  22': 
tan  33°  20'=  .6577 
d.4.2X2      -          8 


tan  33°  22'"-  .6585 


1.0000 


APPENDIX. 


43 


COTANGENTS  FOR  PLATTING. 


Tan- 
gents. 

35' 

4o' 

45' 

So' 

55' 

60' 

Diff. 
for  i'. 

0° 
l° 

2° 

3° 

4° 

.0102 
.0276 

•0451 
.0626 
.0802 

.0116 
.0291 
.0466 
.0641 
.0816 

.0131 
.0306 
.0480 
•0655 
.0831 

.0145 
.0320 

•0495 
.0670 
.0846 

.Ol6o 

•0335 
.0509 
.0685 
.0860 

•0175 
•  0349 
.0524 
.0699 
.C875 

89° 

88° 
87° 
86° 
85° 

2.9 
2.9 
2.9 
2.9 
2.9 

-O 

s 
6° 

7° 
8° 

9° 

.0978 
•II54 
•i33i 
.1509 
.1688 

.0992 
.  1169 
.1346 
•1524 
•1703 

.  1007 
.1184 
.1361 

•  1539 
.1718 

.1022 
.1198 
•1376 
•  1554 
•1733 

.1036 
.1213 

•1391 
.1569 
.1748 

.1051 
.1228 
.1405 
.1584 
•1763 

84° 

83° 
82° 
81° 
80° 

2.9 
2.9 
3-° 
3-o 
3-0 

10° 

11° 

12° 

13° 
14° 

.1868 
•2050 
.2232 
.2416 
.2602 

.1883 
.2065 
.2247 
.2432 
.2617 

.1899 
.2080 
.2263 
.2447 
•2633 

.1914 
•2095 
.2278 
.2462 
.2648 

.1929 
.2110 
.2293 
.2478 
.2664 

.1944 
.2126 
•2309 
•2493 
.2679 

79° 
78° 

77° 
76° 
75° 

3-o 
3-o 
3-i 
3-1 
3-1 

15° 
16° 

i7° 
18° 
19° 

•  2789 
.2978 
.3169 
•3362 
•3558 

.2805 
.2994 
•3185 
•3378 
•3574 

.2820 
.3010 
.3201 

•3395 
•  3590 

-2836 
.3026 
•3217 

-341  1 
.3607 

•2852 
.3041 
•3233 
•3427 
•3623 

.2867 
•3157 
•3249 

•3443 
•  3640 

74° 
73° 
72° 
7i° 
70° 

3-i 
3-2 

3-2 
3-2 

3-3 

20° 
21° 
22° 
23° 
24° 

•3755 
•3956 
•4i59 
•4365 
•4575 

•3772 
•3973 
.4176 

•4383 
•4592 

•3789 
•399° 
•4193 
.4400 
.4610 

•3805 
.4006 
.4210 
.4417 
.4628 

.3822 
.4023 
.4228 

•4435 
•  4645 

•3839 
.4040 

•4245 
.4452 
.4663 

6q° 
68° 
67° 
66° 
65° 

3-3 
3-4 
3-4 
3-5 
3-5 

25° 
26° 
27° 
28° 
29° 

.4788 
.5004 
.5224 
.5448 
•5677 

.4806 
.5022 
.5243 
•5467 
.5696 

.4823 
.5040 
.5261 
-5486 
•5715 

.4841 

•5°59 
.5280 

•55°5 

•5735 

.4859 

•5077 
.5298 

•5524 
•5754 

.4877 
•5°95 
•5317 
•5543 
•5774 

64° 
,  63° 
62° 
61° 
60° 

3-6 
3-7 
3-7 
3-8 
3-9 

30° 
31° 
32° 

33° 

34° 

.5910 
.6148 
.6391 
.6640 
.6894 

•5930 
.6168 
.6412 
.6661 
.6916 

•5949 
.6188 
.6432 
.8662 
•6937 

•5969 
.6208 

•6453 
.6703 

•6959 

•5989 
.6228 

•6473 
.6724 
.6980 

.6009 
.6249 
.6494 

•6745 
.7002 

59° 
58° 
57° 
56° 

ss! 

3-9 
4.0 
4.1 

4-2 

4-3 

35° 
36° 
37° 
38° 
39° 

•7155 

.7422 
.7696 
•7978 
.8268 

.7177 

•7445 
.7720 
.8002 
.8292 

.7199 
.7467 

•7743 
.8026 

•8317 

.7221 
.7490 
.7766 
.8050 
•8342 

•7243 
•75*3 
•7789 
.8074 
.8366 

.7265 
7536 
7813 
.8098 
.8391 

54° 
53° 
52° 
5i° 
<o° 

4-4 
4-5 
4-7 
4-8 
4-9 

40° 
41° 
42° 
43° 
44° 

.8^66 
.8873 
.9190 

•9517 
.9856 

.8591 

.8899 
.9217 

•9545 
.9884 

.8617 
.8925 
•9244 
•9573 
•99i3 

.8642 
.8952 
.9271 
.9601 
•9942 

.8667 
.8978 
.9298 
.9629 
.9971 

.8693 
.9004 
•9325 
•9657 
One 

49° 
48° 

47° 
46° 

45° 

5-i 

5-2 

5-4 
5-6 
5-8 

25' 

20' 

15' 

10' 

5' 

o' 

Cotan- 
gents. 

Subtract  for  cotangents. 
Example. — To  plat  angle  56°  38' 
cot  56°  35'=  -6598 
d.  4.2X3      =        i3 


cot  56°  38'=-  .6585 


6585 


44 


RAILWAY   RIGHT-OF-WAY   SURVEYING. 


TABLE  OF  FEET  AND   CHAINS. 

(i  chain  =  100  links.) 


Chains. 

Feet. 

Chains. 

Feet. 

Chains. 

Feet. 

.01 

.66 

•34 

22.44 

•67 

44.22 

.02 

1.32 

•35 

23.  i  o 

.68 

44-88 

•°3 

1.98 

•36 

23.76 

.69 

45  -  54 

.04 

2.64 

•37 

24.42 

.70 

46.  20 

•°5 

3-30 

•38 

25.08 

.06 

3-96 

•39 

25  •  74 

•7i 

46.86 

.07 

4.62 

.40 

26.40 

.72 

47.52 

.08 

5.28 

•73 

48.18 

.OQ 

5-94 

.41 

27  .06 

•74 

48.84 

.  10 

6.60 

.42 

27.72 

•75 

49-5° 

•43 

28.38 

•76 

5°-  J6 

.  ii 

7.26 

•44 

29.04 

•77 

So.  82 

.  12 

7.92 

•45 

29.70 

.78 

51.48 

•J3 

8.58 

.46 

30-36 

-79 

52.14 

.14 

9.24 

•47 

31  .02 

.80 

52.80 

•IS 

9.90 

.48 

31.68 

.16 

10.56 

•49 

32  •  34 

.81 

53-46 

•i7 

11.22 

•5° 

33  -°° 

.82 

54-12 

.18 

n.88 

•83 

54.78 

.19 

12.54 

•51 

33-66 

.84 

55-44 

.20 

13.20 

•52 

34-32 

•85 

q6.  10 

•53 

34-98 

.86 

56.76 

.21 

13.86 

•54 

35  •  64 

.87 

57-42 

.22 

14-52 

•55 

36-30 

.88 

58.08 

•23 

15.18 

•56 

36-96 

.89 

58.74 

.24 

15.84 

•57 

37.62 

.90 

59.40 

•25 

16.  50 

•58 

38.28 

.26 

17.  16 

•  59 

38.94 

.91 

60.06 

.27 

17.82 

.60 

39.60 

.92 

60.  72 

.28 

18.48 

•93 

61.38 

.2Q 

19.14 

.61 

40.  26 

•94 

62  .04 

•3° 

19.80 

.62 

40.92 

•  95 

62  .  70 

•63 

41.58 

.96 

63-36 

•3i 

20.46 

.64 

42.24 

•97 

64  .  02 

•32 

21  .  12 

.65 

42  .  90 

.98 

64.68 

•33 

21.78 

.66 

43-56 

•99 

65  •  34 

1 

Feet. 

Chains. 

Feet. 

Chains. 

Feet. 

Chains. 

i 

•0151515 

A 

.0606061 

7 

.  1060606 

2 

.  0303030 

5 

•C757576 

8 

.  I2I2I2I 

3 

.0454545 

6 

.  0009091 

9 

.  1363636 

APPENDIX. 


45 


TRIGONOMETRIC  FORMULAS. 

Any  Triangle  (General  Case). 
Sides  are  proportional  to  sines  of  opposite  angles.   ......     (i) 

Sin  ang  opp  given  side :  sin  ang  opp  req  side : :  given  side :  req  side.     .     (2) 
Sum  of  sides :  diff : :  tang  half  sum  other  two  angles :  tang  half  diff.  .     (3) 

Given:  One  side  and  two  angles.     Solve  for  "Req  side"  in  (2). 

Given:    Two  sides  and  angle  opposite  one  of  them.     Solve  for 
"Req  side"  and  for  one  of  the  angles,  in  (2). 

Given:  Two  sides  and  included  angle.     Solve  for  "Tang  half  diff" 

in  (3). 

Given:  Three  sides.     Solve  for  "Sin  \A  "  in  the  following: 


Then,  Sin  %A  = 
Right- angle  Triangle  (Special  Case). 

0.  p          ^       t     b 

SmA  =4-. 


b' 


Cot  A  =  -.     Covers  A  =  ^-^ . 
p  h 


Sec  A  =—      Cosec  A  =  —.      Exsec  4  =  — =— .    Coexsec 4  = . 

b  p  b  p 

In    which    A  =  angle    at    base;    o=base;     p= perpendicular;    h= 
h}-pothenuse;   B= angle  opposite  base;   sine  A  =  cosine  B;  etc. 


NATURAL  FUNCTIONS. 


Radius 


2° 

=  2864  .  93 

3° 

=  1910.08 

4° 

=  1432.69 

5° 

=  1146.28 

6° 

=  955-37 

7° 

=  819.02 

8° 

=  716.78 

9° 

=  637.27 

Sine. 

Tang. 

Secant. 

15° 

.25882 

.26795 

1.03528 

30° 

.50000 

•57735 

1.15470 

45° 

.70711 

I.  00000 

1.41421 

60° 

.86603 

1.73205 

2.OOOOO 

10^ 


75°  -96593  3-732o5  3-86370 


.141592  Log  7T  =  0.497 1499 


LIBRARY 

Due  two  weeks  after  date. 

P       &        |fii-.v 


ic 


r 


